If you took a metal framed gun like a Sig 228 or HK USPC and a polymer gun like the a Glock or aWalther P99 and fired the same factory loads from each, would there be significantly less recoil / muzzle flip  in the metal framed gun?

it varies

for example, alloy/lightweight frames, imo, tend to have more felt recoil than either poly or all steel (or same calibers and/or similar setups); h/w, imo, "NO", not all metal frames have "significantly" less recoil or muzzle flip--maybe less, maybe a tad more

as to muzzle flip, that seems to be more variable on bore axis height (*debatable), ammo (caliber, load, and pressures), etc

other considerations: recoil spring weight and how YOU hold the firearm; the best method in adapting to recoil/handling of any firearm is how one handles it (good form, positioning, and application) does most of the work imo

FWIW: some say that poly frames, like glocks, tend to recoil less b/c the frame can 'flex' and disipitate felt recoil more; all steel frames tend to weight more and also have the same affect

        In theory yes but you have lots of variables.
Bore heigth,grip angle and even the individuals perceptinn all affect the outcome
Some felt recoil is a result of the bullet and gas flying out of the barrel and some appears to be a result of the slide slamming around.
        Different folks have widely different reactions to each gun so in reality you really have to test fire the guns alongside each other to be sure.

FWIW, I have seen many novices who have limpwristed Glocks to the point of jamming them, while at the same time not limpwristing alloy frame guns.  Of course there may have been variables involved such as improper grip, grip size, bore axis, etc.