Considering the fact that this is very simple and relatively easy challenge I think there is no need for the usual "step by step instructions" but only a list of some important things you should know .Still ,since people are used to them so much I made short one:

STEP 1:
Get a Venus Flytrap in your garden by accepting at least one from the the free gifts
The plant has 5 red mouths and when you hover over it has 5 little pictures of red flies listed under "Currently Awaiting" list which means the plant is attracting them.There is also "?" button which you can (should) read

STEP 2:
Put berries on the plates (they eat from both high and low) and attract at least one red fly.The fly will be trapped in the first mouth (which will close) of the Venus Flytrap and it will move from "Currently Awaiting" to "Currently Trapped" list.That means that it is trapped in the mouth and that fly isn't attracted anymore.
*If you have all 5 mouths closed then the plant won't attract any flies

STEP 3:
Find red fly in other garden
When you do this the trapped fly in your garden will get released.The mouth the fly was in will open and it will turn orange
*The color of the mouth ALWAYS gets colored with the next color of the rainbow.For example, if you release green fly the mouth will turn blue

STEP 4:
Repeat steps 1,2,3 with the other 4 mouths and in all colors (red,orange,yellow,green,blue,indigo,violet) until you reach rainbow level.
When this happens there are three things you should know:
1.Once you get your first rainbow mouth you don't have to hunt for rainbow fly to reopen it (of course you can hunt for them anyway but it is not necessary for the mouth)
2.You won't be attracting any rainbow flies until ALL 5 mouths are rainbow colored
3.Once you attract (and trap) all 5 rainbow flies and have all 5 rainbow mouths closed you can harvest the plant and officially finish the challenge.
IMPORTANT NOTE: There is no reward for finishing it.The Venus Flytrap plant gives 20 sq ft of rain forest protected when harvested.
Of course you can keep the Venus Flytrap stored in the storage or in the garden if you wish.

Now the list of the important things you should know:

1.If you don't have any of the free gifts to accept you can :
-Use the self-gifting method where you accept any gift and replace the ID number in the browser area with the number 5042
-Buy one for 10 gold from the place where you send gifts " Buy For Myself (10 Gold)"
-Ask someone that is your FB friend to send it (or befriend other players :) )
IMPORTANT:Since these are seasonal gifts they are available for short time and they can't be accepted after they expire (early November).
For that reason store at least one Venus Flytrap now if you don't want (can't) to work on this challenge right now.
*If you are reading this after November means that you will have to wait for the next year this time

2.What is attracted and what is hunted for :
Currently Trapped- means that you should HUNT those colors of flies in other gardens .Those are not attracted by the plant at the moment
Currently Awaiting-means the garden is currently attracting those colors and are available to spot
IMPORTANT: SPOTTING flies that are not in your "Currently Trapped" list DOES NOT count for your task towards the next color level. It only goes for coloring your picture (but not until you actually attract that fly) and collecting seeds from every 10th.
That being said there is no need to hunt for all colors in advance as it won't help you with opening the mouths of the plant.Exactly the same as the topiaries.

3.The five mouths are working one at the time and always in same order :From bottom right (the smallest mouth) to the top right (the largest one) counter clockwise.This means that the spotted flies will get trapped in that order

4.The attractants are the mouths.The kind of color of opened mouths you have- those colors of flies will be attracted.
*Closed mouths don't attract anything

5.ALL colors of mouths (except red) are attracting flies of the same color and one level of color under.For example, yellow mouths attract yellow flies and also orange flies, violet mouths attract violet flies and also indigo flies..
*In case of the rainbow color : rainbow mouths attract rainbow flies (but only after you have all 5 mouths colored in rainbow) and also violet flies.If you have 1-4 rainbow mouths colored then they only attract violet and NOT RAINBOW.If alongside the rainbow mouths you have other colors they will attract their color and their color one level under.Example: you have 1 rainbow mouth, 3 indigo mouths and 1 blue.Even though the pictures of the flies in "Currently Awaiting" list are: 1 rainbow,3 indigo and 1 blue you are attracting: green,blue,indigo and violet flies ,but not rainbow!
If you had already colored all 5 mouths in rainbow and had 1-4 rainbow flies trapped in them (closed) then you still attract rainbow flies.

6.Flies can only be trapped in the SAME colored mouths.If a fly comes that doesn't matches the color of the mouth it will buzz away free.

7.The flytrap can be stored in the storage AT ALL TIMES regardless if you have opened or closed mouths.

8.IMPORTANT: Just like the bees -flies eat berries.Be mindful of your tadpoles/froglets/adult underwater frogs on your back wall and the adult land frogs in your garden as they (adult land frogs ) will visit you on high plates of berries if you have them available and that might make you lot precious frogpawn.If that is the case, plant and fully dust Dulcia Somniflora before putting the berries so you can deter the frogs.
If you have none spotted or available then don't bother with Dulcia Somniflora
OR use low plates but have in mind that if you have plants that attract raccoon and hedgehog they will visit you all the time.

9.Just like the bees -keep it simple: fewer colors of mouths faster advancement on the levels and better chance of attracting higher level color of fly.
If you have many plants: the more mouths of same color -the better attraction of that color and also the more different colors of mouths the lesser chance of attracting the desired color of fly.

10.Alerts:
-Alerts are on for all flies if garden has them turned on
-The "twins" don't have an alert
-The lower color of flies also don't have an alert.For example, if you have 5 orange mouths the red bee (which is attracted by red and orange mouths) will visit without alert 
-If alert starts and the Venus Flytrap is stored in the storage the alert goes silent

11.For this challenge you need ONLY ONE Venus Flytrap plant (well technically it's not a plant- it's an item like the hives,scarecrows ect. as it can't be watered) .The whole process from red to rainbow happens in all of the 5 mouths.Some mouths might be little "late" and get lower color while other mouths might have higher colors.Unlike the bees (where you need all 5 bees in the hive to harvest it and plant the honey blossom) you can progress on each mouth individually.

12.The challenge ends when you have all 5 rainbow flies spotted in your garden and trapped in all 5 rainbow mouths of the Venus Flytrap which then will be closed .Then you can harvest it and release the rainbow flies.

13.There is NO TIME LIMIT and you can attract/spot them whenever you can/want.
*Links for the Venus flytraps do expire but you can store the Venus trap/s and do this whenever you wish.

14.You can hunt for any color of fly that is on your "Currently Trapped" list to advance as the mouths work independently.There is no order in which you should complete them.

15.Mushrooms: as usual -supershroom is best,if not then pink cap or enchanted mushrooms- in which case I recommend high plates.If you have 2-3 Venus Flytraps you can go without mushroom at all.

That is all.Good luck :)

Just wondering....if you have say 3 rainbow flies in the mouths and 2 indigo flies in the mouths, will a violet fly show up due to the rainbows?

Dorothy, you can't have that scenario as the plant won't attract rainbow flies until all 5 mouths are rainbow.  As per the wildlife guide, violet flies are also attracted to the open rainbow mouths, though.  (Closed mouths attract nothing.)

Hi Stef - one small correction - you do actually still get an alert if a lesser coloured bee is coming to the plate - am in a garden at the moment with all orange mouths and a red bee is on alert :)

urg - sorry, meant fly....

I don't want to work on this challenge at this time so if I want to do this later can I complete this challenge with only one Venus Fly Trap or do I need a bunch like you do with hives for bees? The way I understand this it could be done with only take one trap.

You will only need one, as we know now..! Mike usually has some tricks up his sleeve, lol!! ^_^

lol ... yes this is true. Thank you for your reply!

Peta did that garden also ad another plant with red mouths?

As far as I know and in my experience in the past 3 days with the flies none of the lower level flies had an alert.I never caught any with alert if there wasn't a same colored mouth in garden.But my last fly was caught yesterday afternoon so if they changed anything I don't know about it.
I am absolutely positive about this as I had around 4-5 violet bees coming in mine yesterday morning while I was attracting rainbow flies with 5 rainbow opened mouths and NONE had alert. One even came at 1.57 -no alert.Rainbow flies all had alert.

Kathy ,no you don't need many.You can do it with one.There is no need to save plants with all same colored mouths of each color like we needed with the bees.I surely won't do that but I will store some of the plants in storage in case of a twist later on as Camilla said :)