I have a decent stock of 5.45 (7N6) ammo which is corrosive.

Do stainless steel barrels hold up well against that?

I'd like to build a braced AR 15 for 5.45x39mm.

ANY barrel material is susceptible to the pitfalls of corrosive ammo and should be cleaned accordingly.

The corrosion goes everywhere the gas goes.

Barrel stainless- check
Gas block stainless?
Gas tube stainless?
Gas key and bolt carrier stainless?
Bolt stainless?
piston rings stainless?
Fire control group stainless?

Besides your barrel and gas tube, I don't think any of that other stuff is automatically stainless- it's made for strength rather than corrosion resistance.

There is no magic non-corrodable option when it comes to firearms and corrosive ammo.  Chrome lined/plated comes the closest.

If I were going to build a gun specifically for corrosive ammo I would go with a chrome lined barrel and chrome plated bolt carrier and bolt something along the lines of the Young Manufacturing BCG.  I do not know if there is a chrome plated 5.45 bolt out there though.

That stated, the AK is just plain steel and the boys who use them with the corrosive ammo just clean them out afterwards with water or for a field expedient especially in arid environs were water is precious literally pop the dust cover and pull the BCG and take a piss down the barrel and gas tube.  Gross but supposedly works.

Me - If I run corrosive sardine can ammo in mine I clean it out afterwards fully and completely with hot soapy water just like a muzzleloader down the barrel and gas system, pull the cotter pin and disassemble the BCG and hot soapy water scrub it and it's components and flush the upper and lower receiver.  Dry everything out and then relube everything.  Pain in the Arse but better safe then sorry.

My first 7.62x39 AR upper had a stainless steel barrel, back when corrosive Yugo m67 was cheap and plentiful.

Made no real difference when it came to cleaning though, your BCG and everything else will corrode if you don’t clean it properly, stainless will resist corrosion more than regular steel but it’s not corrosion proof.

Those corrosive salts will get everywhere. I got serious rust on my mag springs after a year of use cause I wasn’t cleaning them.

Corrosive ammo (actually just the primer is "corrosive") isn't that big of a deal.  It just leaves a salt deposit in your gun.  

Any water based cleaner will dissolve the salts and wash them away.  You just have to clean the same day, or maybe the next, after you shoot.  

Scrub everything down with the cleaner, then wipe / drain / Gun scrubber the now salty water away.  Then oil as per usual.  

Hard to beat hot, soapy water.