Neutral game is to setup mines and grenades to prevent rushdown characters from entering your proximity. When fighting other zoners, you want to establish a command by using gunfire M or H, or superjumping and using D+j.H cancelled into gunfire M or H.
I don't know if there's an archive but watching the recent Brazil UMvC3 tournament finals would give you a good idea of how to play Chris.
I'd actually put Hawkeye on Ragtime Shot(Kamikaze) which is the vertical assist, since Chris has good horizontal coverage already. Otherwise that's a solid team.
If your midscreen carry is good, your combo should be something like
Cr.M St.H F.H xx QCB+H > (Dash) Cr.H xx QCB+H > Cr.H xx QCF+H > S.S > j.MMHS > A2 + j.QCF+H > B.H, at this point you should be able to get 2 flamethrowers before the super as well.
- Try not to use Hawkeye DHC, since Gimlet scaling is terrible late in the combo.
- Chris' best normal is Cr.M, good hitbox, hard to punish, good anti-air, hitconfirms into St.H 95% of the time. Counterhit Cr.M also links into Cr.H, which is useful to know since you may get a wrong input sometimes but still be able to combo off of it.
- Chris' blockstring is pretty predictable and tends to be unsafe even when cancelled so when you're applying pressure make sure to watch out for your opponent's pushblocking habits since Chris can be punished by certain characters like Dormammu.
- Generally use Mine (L) to end blockstrings because the pushback it causes is very hard to punish and I think it's -4 on block.
- Only use Gunfire (L) sparingly like predicting a tri-dashers approach because it has an abysmal startup and scales combos massively.
- For this team, put Chris on Gunfire assist because it is the best THC for this configuration.