Of course. You should flirt with all women. (Exceptions might be female authorities and nuns, but even then...). Of course calibrate how much you flirt to the girl and situation.
What I think you're really asking is should you date girls in your class. To that I say YES, but you probably want to keep it to one at a time (especially if you go to a small school). Even if you fuck it up with every single girl in the class and they all look down on you the rest of the semester, you'll have gained valuable experience. And that's worst case scenario.
I'd advise being known as a cool, flirty guy, and keep it at that. Be discreet with whoever you go after. This helps save both your face and her face should things get wierd, communicates the right message, and allows you to go after other girls later.
And move fast. Not street game 5 minute number pull fast, but talk to her for a bit and get her number within two classes. I've gotten girls in bed after getting a number the first time I talked to them in class. This might not be applicable right away since it's freaking April.
Cool?