Don't do it, for a couple of reasons.

a) She's now stressed out wondering who sent her flowers. Now she has to be on guard against woo-throwing from every ostensibly friendly dude in her life in case those flowers are from someone she's not interested in. When she eventually finds out it's you, you're gonna be that guy who stressed her out by sending anonymous flowers, and you're gonna come off a little obsessive. Honestly, sending flowers to somebody you're not dating is way too intimate, and she's gonna find it creepy.

b) You are going to deepen whatever feelings you have for her by engaging in anonymous romantic gestures. You'll spend a bunch of your time for days on end wondering what she thought. You'll be totally miserable. Meanwhile, she doesn't know it was you who sent her flowers, so her feelings towards you won't have changed either way. That's a fast track to depressive-unrequited-love-land.

If you like her, just ask her out on a date directly. If she says no, be prepared to take it like a man, acknowledge that rejection gracefully (the FIRST time), and leave her alone. And if she says yes, hooray for you both.

Honestly it sounds like you're crushing super hard; you need to temper your expectations a LOT or this is gonna blow up in your face and be really unpleasant for you both. You're not in love with her, she's not your dream girl (NOBODY is). You're just interested in her, and you don't know whether she's interested in you. Slow down, play it cool and be prepared to move on if she's not interested in you. Or even better, honestly, step back from dating/romantic stuff altogether and work on yourself--it's not healthy to put somebody on a pedestal the way you're doing, and you're gonna be a lot happier when you're in a mental space where you're not thinking about anonymously sending flowers to acquaintances. Best of luck, hope that didn't come off too harsh--being single is hard for everybody.