Well, you do have to use a bit of precaution and common sense, in addition to the helpful hints from the site I linked. Here are some tips:
If you're planning on showing cock, DO flash near the end of Bourbon street where the gay bars are. They'll be plenty of others doing the same and there's safety in numbers. DON'T flash at the neighborhood McDonald's.
If you're planning on showing boobs, DO flash from balconies of hotels or if on the street, in the safety and presence of a few good comrades. DON'T be the only gal alone (or with one guy) flashing in the middle of a crowd of college frat boys, jocks, and other assorted mortals - unless you want about fifty hands trying to cop a feel right afterwards.
If you're planning on showing either, be cool and check out the scene as to what's going on first. Again, there's safety in numbers. If you see flashing and bead throwing going on, everybody's smiling, laid back, and having a good time (and you can't see any cops in the immediate vicinity) then you're probably good to go.
Most cops will ignore what they see on Bourbon and Royal on Mardi Gras day. Every once in awhile though there may be one who's ticked off or having a bad day, SO, do have a good time, follow their directives and DON'T try your luck by flashing your stuff right in their faces.