I've never heard of a moped carb flooding. Assuming too much fuel is in the cylinder (i.e. the bike reeks of gas when you pedal) from the choke being on too long, just turn the choke off and pedal for a bit with the throttle closed (or the spark plug out). There is usually a drain screw somewhere in the lower portion of the carburetor if you'd like to drain the gas out of it.
However, I think that your moped is probably not starting for another reason. The number one reason a moped suddenly ceases being easy to start is an old spark plug. Hit the hardware store and buy a half dozen (yes 6) spark plugs for your moped. Whenever ANYTHING engine related starts acting up, the first thing you should try is a virgin spark plug. If you ride a lot, expect to go through two or three plugs a year. Throw away old plugs. They're cheap, don't keep any plug you have doubts about hanging around.