A brake is the device that slows down a bicycle.
Anyway, a coaster brake would be incompatible with a fixed gear hub.
I understand that there have been conversions of 2 speed coaster brake hubs into 2 speed fixed gear hubs. No brake.
You might ask about 2 speed hubs in the Singlespeed & Fixed Gear forum here at BF.
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Bacchetta Giro A20, RANS V-Rex, RANS Screamer