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The muzzle is threaded 5/8-24, and you would just want a muzzle device listed with the same thread pitch and compatible with 30 caliber, or 7.62/308.
I emaild them asking if there was any reloading info that they recommend for the barrell. They told me the barrel is bored at .308 not .311 "7.62X39" they used factory ammo with .308 diamater. It still shoots fine about 1.5" to 1.9" with hornayd black 7.69X39 ammo.
Here is the info I got from Faxon website https://faxonfirearms.com/16-gunner-7-62x39-mid-length-4150-qpq/
Quality is imbued into our barrels from the start. We start with the best materials, either certified 4150 Mil-Spec steel or 416-R Stainless. From there, each barrel goes through a battery of tests at each operation until finished in Nitride and final inspected. All barrels are individually checked for headspace by precision custom hardened gauges.
Barrel Material: 4150 Certified Gun Barrel Quality Steel
Barrel Type: Button Rifled
Barrel Caliber: 7.62x39
Barrel Twist: 1:8
Barrel Length: 16”
Barrel Profile: GUNNER
Barrel Gas System: Mid
Inside Finish: QPQ Nitride
Outside Finish: QPQ Nitride
Muzzle Thread:5/8-24 TPI (Threads Per Inch)
Gas Block Diameter: .750"
Gas Block Journal Length: 1.9"
Barrel Extension: M4
Weight: 1.48 lbs
Magnetic Particle Inspected!
11-degree Target Crown