I am considering Ft Riley as a duty station. I am a single Soldier who is a E-5(P)with household goods. Am I authorized off post housing?

I believe that depends on the barracks capacity.

I ran into this case a couple years ago and the barracks were full during barracks renovation and all SGTs and above were authorized BAH to move out into town.

When the barracks were completed, SSG and below had to live in them ... one of the exceptions was if you had household goods from prior to a PCS move.