In first place, I don’t understand why anyone would want a .357/.38 AR. And you’d think if there were any “need” or market for it, someone would have done it by now. The AR system has only been on the market for 40 years.
Secondly, I’d think that anything you could do with a .357/.38 AR could be done nearly as well with a 9mm. I wouldn’t think any possible advantage would be worth the hassle of trying to cobble the thing together.
All that said, however….
If you want to pursue this, your biggest problem is prolly going to be a suitable magazine, and then a suitable bolt. I can solve both those problems for you in one stroke.
Back in the mid-‘70s, Jeff Cooper sort of “magnumized” the .38 Super by making brass from cut-down .223 empties (which of course is much stronger in the head area than normal .38 Super cases). IIRC he was getting near-.357 velocities, at least with lighter bullets. You could do the same thing. You could reline a shot-out .223 barrel to .357 bore and then ream it to .38 Super. You might even be able to rechamber a standard 9mm barrel (not sure if this would work or not). You could even go Cooper one better by cutting the .223 brass to longer overall length, as you are now limited only by the AR .223 magazine, not the shorter handgun mag.
Of course, if you keep the case at normal .38 Super dimensions, you could then carry a handgun chambered for the same ammo.