There does not appear to be publicly available Fujifilm documentation for the X-series Wi‑Fi protocol, at least based on the answers provided. One answer suggests contacting Fujifilm directly, but otherwise reverse engineering seems to be the main path people have tried.

Community findings indicate the camera may act as 192.168.0.1, with the phone app opening a TCP connection to port 55740. One user observed what looks like a message-based protocol where the first 4 bytes represent packet length. Another answer points to a GitHub project attempting to reverse engineer the protocol for the X-T10.

So, the practical answer is: no widely published official protocol documentation was identified here; some partial unofficial details exist; and custom development likely depends on reverse engineering the app-camera communication. If you pursue that, review Fujifilm’s terms and any applicable laws before sniffing or analyzing traffic.