I've played this match up pretty pretty often. And I just hate it.
On of my crew mates is maining DK and in local tournements the grand final
highly likely to be me against him
Nevertheless I still choose GaW against DK.
First of all: It really depends on the map! If you have a good counterpick
the match up can be very fun. (I really like to play DKs on Rainbow cruise^^)
On Yoshis Island its a complete nightmare. If you've got wrong DI you are going DOWN xD
Don't forget to not pick Corneria. Its one of the best GaW stages but also one of the best DK stages.
As Tero already said the range is the biggest problem you have
Ftilt, fsmash, bair, dtilt, and down b all have ridicilously good ranges.
If your spacing isnt perfect you'll get punished imediately which is a huge
problem since DK can finish you at very low % and you on the other hand
need a large amount of damage to finish him, especially if his DI and momentum canceling
are good.
Also really annyoing are the stupid super armor frames of the neutral B. don't forget about them.
So your chances are at the air game. try to keep him in the air with your upair and get him with your nair.