If you can prove their negligence caused the incident, then yes, you could sue and win. However, you have to prove that it was their negligence that caused the incidence. This stuff does happen... without negligence occuring. Really, you are responsible because you should have renter's insurance. Renter's insurance is pretty cheap (around $10-$14/month) and will protect all of your belongings. I've had two friends who refused to pay for insurance and then lost everything in a fire -- not a good situation.
In order to get anything from the apartment, you'll have to sue them... and you'll need to have proof that their negligence caused the flood. Otherwise, you simply need to replace your own items (and seriously consider purchasing renter's insurance). Good luck to you.