Just don't conflate between a flinch, and poor recoil management.
A flinch takes place before the shot takes place. That is an anticipation error in technique and is correctable.
Recoil management occurs obviously after the shot. Having a consistency in recoil is testimonial to consistency in technique but depending on the cartridge and rifle set up, following the shot can be difficult, but not impossible. The more you do it, the easier it gets imo.
Flinching from pain afterwords has no bearing on the shot if anticipation did not occur. Though, its rifles these days are not like shooting a mosin nagant with a steel stock. As little sacking up might be necessary.