Getting married while one partner is incarcerated is possible but it requires working within the facility's rules, and those rules vary significantly from one institution to the next.
The first and most important step is for your fiance to contact the chaplain directly. The chaplain is the person inside the facility who handles marriage requests and knows exactly what the process looks like at Arkansas Valley specifically. That conversation will tell you quickly whether marriages are permitted there, what the requirements are, what documentation is needed, and what the timeline looks like. There is no point navigating the outside logistics until you know what is possible on the inside.
If the chaplain confirms it can happen, the process typically involves a formal request that works its way through administration for approval. You will likely need to obtain a marriage license from the county, which in the Arkansas Valley's case would be Crowley County, Colorado. That license has to be in place before any ceremony can take place. The chaplain or a designated officiant at the facility would then perform the ceremony, usually with very limited guests if any are permitted at all.
The warden's office has final say on whether a marriage gets approved. Having your fiance make the request respectfully and through the proper internal channels is the approach most likely to get a yes.
Start with the chaplain. That one conversation clarifies everything else and gives you a real roadmap to work from.