How do you obtain a shaving profile or no shave chit in the military?

AR670-1 lays out the religious process. The Chaplain and your BDE level commander validated it.

Your medical provider determines if you need one and it’s entered into MEDPROS. You then have access to a printed copy which will warm your 1SG’s heart.

Depends on whether you are doing it for medical or religious purposes. You would go to medical or the Chaplain depending on what’s applicable

If there is something actually wrong with you then see your PA. If you want to be part of the cool guys then go try out for one of the elite forces.