Just when I think I get those flowers down 500 more show up. How and why are they appearing?

As you add Flower value to your island, how many more Flowers you need to get to the next level will approach zero. When it reaches zero, you will level up (number in red to the right of your profile picture). Then any additional Flower value will roll over, such that it will show how many more Flowers you need for the next level.

How many flowers you need per level can vary from 70-530, depending on which of the 5 scenes in the chapter it opens. If you want to plan ahead, it generally takes about 1500-1700 flowers for each chapter.