So I have done several testings on how you can beat Shinobi, specially countering his kick and making it useless. Here are the results:
Conqueror cannot punish the backflip, but can dodge bash a heavy follow-up attempt:
Shugoki can light attack through the kick, tank the hit with hyper armour and prevent heavy followups with his headbut and follow the backflip with the headbutt.
LB cannot punish a backflip after a whiffed kick but can prevent followups with a shove light.
Nobushi can trade the kick with viper's retreat or hidden stance the kick into light-light preventing all followups. This combo also tracks the backflip () ()
Peacekeeper cannot punish the backflip with side dodge. The timing seems to be extremely tight for the side dodge attack to hit the shinobi on the kick
You can however punish the backflip by a non-attack dodge followed by lunge.
Raider can dash-GB the kick. Raider can stunning tap the backflip followup if he dodges but doesn't GB
Orochi can dodge attack the kick. It tracks the backflip and interrupts the heavy followup
You cannot trade a double light with the kick, the kick landing will interrupt the second light.
Valkyrie cannot side dodge attack the kick. I don't believe the i-frames are applied or something, because she'll get hit by the kick every time. She can however dodge, then light or forward dash attack to punish a backflip.
Warden can dodge bash the heavy followup into his mixup
He cannot truly punish the backflip as the shinobi recovers from backflip in time to block side or top light
Beserker can dodge light into heavy top.
Shinobi, on top of forcing these reactions can always go into his 50/50 from neutral. You can delay the kick by a fair amount so that they MUSt do everything on reaction.
To conclude, you're SoL in terms of punishing the kick + backflip followup unless you are Shugoki with HA up, PK, Orochi, Beserker, Kensei, Valk, and Raider.