It takes a minimum of 7,905 steps to hatch a Druddigon egg, or 31 Egg Cycles without using Flame Body. (1 Egg Cycle=255 steps)
There are actually a few ways to speed up the process of hatching. If you have a Pokemon with Flame Body in your party, (e.g.: Litwick) the number of steps it takes to hatch an egg is halved!
Also, if you're aiming to prioritize this Druddigon egg over other eggs, (if you're hatching other eggs) then don't receive or hatch other eggs, because for every egg you receive/hatch, the egg cycle of all eggs in your party are decreased by one!
Also, for future reference, you can search your desired Pokemon in the black search bar of this website and find stats, abilities, and even the egg cycles of your Pokemon.
Hope I helped!
Bulbapedia: Egg Cycles