Log on to the APAN site, https://wss.apan.org/s/AFCB/default.aspx
Fill out the OCONUS Travel Request, Form 500
Submit it via the site to this email address, firstname.lastname@example.org
The DoDI 1304. 28 outlines the relevant requirements:
6.6. Visits of Endorsing Agents to military installations in overseas areas are encouraged to enhance the spiritual welfare of military personnel, particularly at seasons of special religious significance.
6.6.1. Such visits shall keep the religious organization aware of the ministry of the organization's chaplains and the spiritual and religious activities of the military community and permit Ecclesiastical Endorsing Agents to maintain their professional relationships with endorsed chaplains.
6.6.2. Such visits shall be at the discretion of the commander(s) of the installations involved.
6.6.3. The Ecclesiastical Endorsing Agents who visit installations representing their religious organizations shall do so at no expense to the Government. The Ecclesiastical Endorsing Agent shall be afforded protocol privileges appropriate to those of a civilian employee in the grade of GS-15.
6.6.4. The Military Departments may establish procedures governing the visits of Ecclesiastical Endorsing Agents to overseas installations. The AFCB may provide administrative assistance in arranging such visits.