Basic Combos

Ky's basic combos are pretty easy, so most of the time you won't have to practice on execution at all.

[Gatling Combo] -> Sweep -> CSE

Most of Ky's ground combos will pretty much look like that. After Ky combos into a sweep, he cancels the sweep into a CSE to maintain the initiative and to force the opponent to block it on wakeup. The gatling combo you use to combo into sweep doesn't really matter all that much, but if you get too greedy with your gatling combo, you may not be able to combo into sweep.

[Gatling Combo] > Stun Dipper > Okizeme

In case the Gatling Combo knocks your opponent too far back, you use a Stun Dipper instead. Make sure that both hits of the stun dipper combo; if it doesn't then that means you were too close. Such combos usually do more damage than gatling combos into sweep, as most of the time you hit them more. However, the problem is that such a combo leaves a burst point (right before the second hit of the dipper) where an opponent can safely burst out of your combo and regain the initiative. Furthermore, in a mid screen situation you usually can't follow up with a CSE, so to retain the initative, rushing in and doing a meaty attack (usually 6HS or JD) is called for, unless you have enough meter to do a FRCed CSE and follow up with it.

Hit confirm > Stun Dipper

On a far S comboed into 2S, you can combo this into stun dippper if the edge is hitting. If they block it simply do a stun edge instead, although there are situations where a stun dipper into FRC or even a Greed Sever may be better. If you can do this while they're in the corner, you can RC the second hit and then go into a VT loop.

Greed Sever Combos

For average weight to the heaviest characters, use:
Sever > close S > 2HS > HSVT
Sever > close S > Sever > K or P > HS > HSVT

For any character lighter than average weight, use:
Sever > 5S > Air Combo

Unfortunately, these combos are very character and location dependent, so you'll have to sorta learn where and when you can do this. In some cases, you may not even be able to combo a standing P off of the sever, and in other cases you may be able to do 6P > Close Slash or HS.

6K and combos off of 6K (close S > 6K loop)

Ky's 6K is a semi oddity that sorta violates the gatling chain in that it will only link into certain things, but those things are a bit odd. 6K does a good 36 damage and gives you a 7 frame advantage on hit (which is awesome because Ky's right next to the opponent on hit). So if timed correctly, you can take advantage of this 7 frames and link into something else. Note that on a crouching character, Ky's 6K will actually give him an 8 frame advantage on hit since it will reach the opponent one frame earlier. On the latter case, that is why the 6K > Close Slash is a lot easier than in the former case, and since 6K doesn't really knock the opponent back too far, you can usually get a good 2 or 3 reps off of it. Thus:

Standing character:
2K > Close S > 6K > 2K > Far S > Stun Dipper
Dash 2K > Stand HS > 6K > Close S > Stand HS > Stun Dipper
Dash 2K > Stand HS > 6K > 2K > 2D (> Sacred Edge or CSE for okizeme)

Crouching Character:
(Close S > 6K) * 3 > 2K > Far S > Stun Dipper
(Close S > 6K) * 3 > 2K > 2D (> Sacred Edge or CSE for okizeme)

Things that will link off of 6K:
5 Frame moves - P, 2P, K, 2K (easiest to do if they reach), Stun Dipper (although you usually can't make both hits combo)
7 Frame moves - Close S, Sweep
8 Frame moves - Sacred Edge (yeah, you can do that on a crouching character but it kinda sucks)

Doing a 7 frame move off the 6K while opponent is standing is difficult, but those do the most damage so go for it if you can do it consistently. Crouching character is different though; go for the 7 frame moves in that case since it's rather easy and no practice is really needed. The only thigs you really need to watch out for are the distances between you and your opponent.