Just like viewtiful_dru said, gotta use LP fireball more, especially after you knock them down. The instant stomp is something you'd do if you're really kicking their ass. You seemed a lot better than the other guy so it was fine, but normally you'd want to throw a LP fireball and then mixup between a low hit, overhead, or dash > legs.
EX legs combos were good, but you need to be able to combo to ultra if they're in the corner. That's basically Chun's main objective. 2nd objective would be to bait a fireball and ultra through it. No random ultras!
You're jumping forward way too much. It's not that bad against Gouken, but normally you'd want to jump straight up and hit HK, I don't think I saw this at all. Just need to play safer and turtle more. Overall pretty good though, nice combos and stuff.
A couple of other random things, HCB+K is very safe, you can follow this up with cr.MK>kikkoken without too many hassles. LP (standing or crouching) is +3, it's excellent for setting up throws. The only mega unsafe moves that Chun has is ultra, EX SBK, and upkicks, so make sure that if you use these, they're guaranteed through combos or anti-air (for EX SBK), or used as punishers on their unsafe moves.