Black powder itself is not hygroscopic, it's the salts left after black powder is fired that are. The main charge in a flintlock is no more susceptible to wetting than that in a percussion arm, it's the prime that is a concern. Priming powder placed in a perfectly clean and dry pan will last for hours on the wettest day if the above precautions are followed. However, if even a little of the residue from the last shot is left when the prime is placed, it will turn to soup, quickly. Simply make certain that pan is really clean and dry, and you'll have no problem.
Flintlocks are as safe as any other gun, and as dangerous.
All customary safety precautions used with any other black powder arm should be followed. In addition, it's possible to fire a flintlock by dropping the hammer on the frizzen when the pan isn't primed. Shooting glasses are recommended. Advise those around you to stay clear of the lock-side of your gun when you shoot. Special Thanks to Bob Spencer for the vast majority of this work, and Coon 'n Crockett Muzzleloaders for use of their graphic.