Yes, being incarcerated does not strip someone of the legal right to file for divorce. It complicates the process but it does not make it impossible.
The facility itself is not going to help him pursue a divorce. If he asks, the standard advice from jail staff will be to wait until he is released and handle it then. That is the path of least resistance for everyone involved except him.
If waiting is not an option, he needs to file a Petition for Divorce in the appropriate court and have it properly served on his current spouse. That service of process is the step that gets the legal ball rolling. From inside a county jail, coordinating paperwork, court filings, and service can be logistically challenging but it is doable with the right help.
The most practical route is hiring a family law attorney to manage the process on his behalf. A straightforward, uncontested divorce handled by an attorney typically runs a few hundred dollars, though costs vary by state and complexity. The attorney handles the filing, the service, and the court communication, which removes most of the logistical burden from someone who is incarcerated and has limited access to the outside world.
If money is tight, some jurisdictions have legal aid services that assist low-income individuals with divorce filings at little or no cost. His case manager at the jail may be able to point him toward those resources.
The sooner he gets the petition filed and served, the sooner the clock starts on the process.