I had got the extremespeed dratini from the dragons' den and it's now it's a dragonite, but I messed up all the EVs and want another one, so I put a dragonite (extremespeed) and a dratini in the day-care but when they have eggs the dratini that hatch don't have extremespeed. Why?
If the Dragonite you got was female, the resulting offspring won't inherit any egg moves.
Egg moves are only passed down by the male parent. You need a male Dragonite (or any previous evolutions) with Extremespeed to be able to breed the move.