We have a
lot of MKs here, so I've gotten to play this match-up more than I'd like to.
Note: I've had no practice vs someone who can infinitely dimensional cape, so I have no idea how much worse this makes it for DK(My guess is definetely worse though.)
Edit: Apparently the IDC is getting banned everywhere like wildfire, even here.
Really this entire match-up can play out a lot differently at times, since it mostly depends on how well versed your MK opponent is vs DK. Here's an idea of what to expect on both fronts:
Your MK opponent isn't as experienced vs DK:
MK players who haven't had much DK experience will often not know exactly how to approach other than the standard MK approach. Using this against them is key to beating them. Bairing will be more effective, and trying to land Fsmashes won't be as nerve wracking since it may not always lead to being juggled like mad. If they keep coming at your Bairs, just go with it and keep mixing up all of DKs good spacing attacks. Generally they won't be able to grab-combo you into a zillion Uairs if you do get struck out of a Bair, but most will still know to at least whornado you. If they forget to whornado you when they can, don't remind them. Sometimes when losing they may attempt to start spamming whornado. Just try to predict/escape it and punish it with a finsher. It only takes one good Fsmash/DK punch/Usmash to kill them.
Always try to retain position on the stage.
Even vs an lesser MK player you could lose if you keep losing position.
Your MK opponent knows DK like the back of his hand:
Bair's use here really depends on what kind of game plan MK has vs DK. What matters most is MK's approaching game plan. If you start to camp some SH Bairs vs a MK that knows DK really well, he will avoid attacking through your Bairs and use the fact your not Ftilting or grounded as a time to close in position on you to either whornado around through your Bair, or attempt to get through/around your Bair and grab-combo you. Also Bair can be risky vs MKs that know exactly when and where to strike you, because if you get struck while Bairing in the air it can lead to a whole mess of things: whornado, Uair juggles, and most often end in a quick shuttle loop off the stage. Also be prepared to avoid MKs who attempt to glide swipe you, as it can be
half a mindgame to gain position on you since they land so close after they do it. The best answer to this is generally an Ftilt upwards to their face. If they do get in close with a glide swipe, they may follow it up with a whorenado or some Dtilts, leading to a trip, which leads to combo hell. Glide swipes can come from grounded shuttle loops, or just normal jumps. Just always be prepared to swat them down, and to not allow him to land too close from them. This doesn't mean Bair is useless though. A rule of thumb could be: If your opponent is attacking into your Bairs, keep Bairing. If you notice he's trying to get
around them and gain position on you, then don't Bair as much and be prepared with more Ftilts.
MK could probably use the above information against DK...
Basically with the right game plan vs DK, MK can really make this match-up a nightmare.
Also DIing out of the tornado needs a bit of an explanation:
When the MK player hits you with a tornado you will need to pay attention to the current momentum of the tornado itself. You'll want to DI away from where their current momentum is heading. If MK tornados to the right, DI left(unless this would suck you back in of course). If your caught dead center in it your usually stuck through the whole thing, but sometimes they will swing wildly back and forth, and one big swing could allow you to escape. If they just rise it straight up though, your usually stuck for the whole ride. If you get caught by the outer perimeter of it, they will usually(should) tornado
at you so you can't DI out so easily. If they don't, or your just too far to the outside of it, DI away from their momentum, and this should release you allowing you to go for a nice juicy Fsmash/Usmash. Just make sure if you escsape the tornado early they may still try to pick you back up, and if they can't get you they will tornado towards a platform so they can appear on the ground. Try to either land an Fsmash/Usmash/etc if you can!
I've used a mix of R.O.B. and DK to beat MKs, but have to say R.O.B. is a bit better at it than DK. Neither like the match-up though.
Also if you simply cannot beat MK with DK, try seconding ZSS for MKs. ZSS is a solid MK counter.
I'd say at worst this match-up is somewhere around 65-35 in MKs favor.