It's pretty even, 55 in favor of DK. But that's only if Kirby get's the first hit so DK has to approach. Any other case would be 60/40. Seriously, any match up where one character has to be over 110 to kill the other one while the other one needs to be 85+ isn't even.
Ummm... MK vs Kirby, Ganon vs Kirby, Mario vs Kirby, Falcon vs Kirby, Ike vs Kirby, Lucas vs Kirby, Probably Luigi vs Kirby, Wario vs Kirby, to name only Kirby matchups. Would you put ALL of these against the character who kills a lot earlier?
As for DK, I'll admit I only have limited experience with this matchup, as I tend to pull out Mario vs DK, but the few times I have played them, I seemed very much able to combo Dthrow into a few Utilts into some Uairs. However, they probably could have escaped earlier... I don't really know.
Also, everything else you guys mentioned seems spot on.
Can we inhale the ape out of his Bair by any chance?
I think FC actually beats his Bair, though he can probably DI out of the second hit then punish our lag, so that might not be a good option.
It's pretty easy to gimp DK though. Yeah, as someone said, they'll be on the lookout for it, but their recovery is bad when it comes to vertical range, and the landing lag on it is atrocious, which doesn't give them a big window to use it when recovering. All they can really try to do is headbutt stall, but we should have enough jumps to wait it out and still drill>footstool them. Personally, I think this is the biggest thing going for us in this matchup. If he tries to recover higher than the stage, don't even bother trying to get above him and drill, just wait on the ground and Fsmash him during his lag.
Also, get DK's power if you can. It's a great kill move that gives SA, and can also be used to survive punches/smashes (Best way to punish a Fsmash if you're in range is with this power). Just remember your range is MUCH smaller than DK's.
EDIT:
Then from my understanding, Fthrow->uair is inescapable, and after that, NOTHING is guaranteed.
The Uair isn't guaranteed on every character either. Mario/Marth can UpB, Mario/Luigi/Shiek/Yoshi/probably Samus can Nair, ZSS can DownB, Snake can pull a grenade, MK *might* be able to do an aerial or SL, and there's probably other things I don't know about/am forgetting at the moment.
So yeah, general rule: fast move, Sex kicks, and fast moves with invulnerability beat it.