Two weeks without contact from someone who normally calls every few days is worth following up on, and calling the facility directly is exactly the right move.
When you call, ask to be connected to one of the following people in this order of likelihood to be helpful: the unit secretary, the counselor assigned to his unit, his case manager, or the warden's office. The unit secretary and counselor are often the most accessible and the most willing to share basic welfare information with someone calling out of genuine concern.
Keep the tone of the call calm and straightforward. Identify yourself, explain that your friend normally contacts you regularly and that you have not heard from him in two weeks, and ask simply whether he is okay. You are not asking for case details, disciplinary records, or any private information. You are asking whether a person you care about is in good health and not in crisis. That is a reasonable ask and most staff will respond to it humanely if you approach it that way.
Be prepared for the possibility that they confirm he is fine but cannot tell you more than that, or that they decline to share any information at all citing privacy policies. If that happens, sending a letter is your next best option. A letter asking him to call or write back when he can puts the ball in his court without requiring the facility to disclose anything.
The most common explanations for an unexpected communication gap are a stretch in the hole, a transfer to a different unit or facility, a medical situation, or simply a period where he has withdrawn and is not reaching out. Most of those resolve on their own. The call to the facility gets you clarity faster than waiting and wondering.