Nix89 is right - it used to be that all children were enrolled at their First Communion. So, since not all priests are Carmelites or Franciscans, and assuming that these enrollments were valid, then any priest can enroll.
Also, the Blue Army travels from church to church in my area praying the rosary one Sunday each month. Afterward, they ask the priest at whatever church they’re in to enroll participants in the brown scapular.
BTW, I love my brown scapular and love that I’m enrolled! My husband is going to be enrolled in two weeks when the Blue Army returns.