In fact, if you want to attack after a TK j.41236S, you'll need to FRC it.
Off a jump-in j.41236S midscreen, you can do 66 5P 5S 2HS IAD j.S (you want it to hit very low to the ground) j.41236S 669 j.S j.HS j.D slight delay j.41236S 669 j.S dj.S 63214HS (you'll have to cut it short vs May, I-No, Dizzy and one or two other characters)
There are better variants depending on the character, but I'm a bit lazy to post them all here, the combo thread covers some of them, but not the best ones IMO.