Flourish doesn't have anything to do with the flower opening - that is called flowering or blooming. Bloom means pretty much the same as the word flower - but is usually used for flowers which are well cared for. But you can use flower and bloom pretty much in the same way.
Flourish means that something does very well. Like "a plant flourishes" means it is growing strong and looks good. You can use it for people as well. For example: She went on a vacation and is flourishing that close to the beach :)
Oh thank you for explaining, I appreciate it a lot!! <3 And I love the word "bloom" ! :3
You are welcome. My pleasure :)