Print:

Flower_Red.stl (Flower Pot and Action Button, I printed mine in Red)
Flower_Green.stl (Stems and Leaves, I felt like these should be green)
Flower_Petals.stl (The Flower, red and then swapped mid-print to yellow)

There is also a full tray available if you want to print them all at once or you can do each piece individually.

Now, I have provided assembly pictures over there on the left. Unfortunately the process has changed slightly. In the pictures it shows me stringing one piece of string through the entire flower. What I recommend now is that you put the button in the center of the fishing line and then bring up the two ends through the flower. So you are threading two ends through the flower, but it is one piece of fishing line.

Doing it the way in the picture makes it way too hard to tie at the end.

Okay, Got it?

Ok, so, by now you figured out you need some fishing line, well, you also need a spring. The button is designed for a spring with an inside diameter of a little over 14 mm and about 20 mm tall. The fishing line, you should start with pretty long, I went with around a meter, but this was maybe too much. Use as much as you want, just make sure you have enough to make it through the entire length of the flower. There is no harm in going too long, we cut off the excess at the end.

So, first string through the button, bring up both sides of the string through the spring. Now mount the spring so it sits around the cylinder that is on the button. Then Bring the fishing line ends through the hole in the pot.

Now string some stem segments on the line. I started with three, but you do as many as you want of course. Next place the leaves where you want them. I have also included single leaves, if you want to use them. After the leaves are on, you probably should add more stem segments.

Last is the flower. There are two holes in it, bring one end of the line through one hole and the other end through the other hole. Now both ends should come out of the top of the flower.

Now, this is the difficult and important part. You may need an extra pair of hands to help tie it. It is useful to have someone push in the button while you tie it, because the knot you tie has a tendency to slip a little and it won't work if it is at all loose. So, with the button depressed, tie the two ends together in a square knot and pull them so they go pretty tight. If you want to be on the safe side and make sure it stays tight, you can add additional knots. Now cutoff the excess fishing line!

And now you should have a working 'push puppet' flower. Enjoy!

PS - If anyone knows a better knot to use, one that can only get tighter, please post!