As a guy who's thought of doing something like this in the past and decided not to, here's why:

1. Most women consider getting flowers sent to their work only appropriate for certain days (Valentines is usually the only one).
2. A gesture like this is more likely to dig you deeper into the friend zone if you're leaving it ambiguous and not making your intentions clear.

Instead of using an overly dramatic gesture like this, which is really only appropriate if you're in a relationship with the girl, see if she's interested in other ways.

Next time you hang out with her, make her laugh and hold her eye contact a few seconds longer than usual. See how she reacts. If she also holds eye contact with you, and there's a noticeable few seconds of silence, that's progress right there.

This part depends on your existing friendship with her. If you are not usually physical when around her (hugging, tapping on shoulder for emphasis, etc), then see what happens if you become more touchy and physical. Nothing over the top or inappropriate, kinda like how you would be touching another guy. Watch her body language when you do this, and see if she's receptive to it, or closed off. Easy way to gauge physical receptiveness is if her body becomes more relaxed and open, whereas non-receptive body language is more closed off (crossed arms, crossed legs pointed away from you, etc). If you don't know how to read body language, google it. Or go to a bookstore.

You can always see how receptive her friends are to you and her dating. If you're close to her friends, they might think it's adorable and help you by planting a few seeds. This accelerates the above two processes.

Beyond that there's a few other ways to get out of the friend zone or whatever you're stuck in with her. This should get you started, and if the rest doesn't naturally fall into place, there's still a few extra things you can do, but remember to weigh the value of going the extra mile when you can just spend that energy on another girl.