Good luck with your LE career. Many of us do use snugly fitting open top pouches; they're issue from Alaska (most departments I see up there) to Jacksonville Florida. With the flapped type, still required by many agencies, what I found worked best was to bend the lip of the flap below the button outward. Magazines were placed bullet noses forward. The heel of the support hand would pop up the flap as the hand swept to the magazine, saving an extra movement for unsnapping. Thumb and middle finger grasp the body of the magazine, index finger outside the front of that cell of the pouch. As the magazine clears, turn palm up, insert, and carry on.
To get that lip bent on a leather pouch, just dampen that part of the flap, bend it up, and leave it overnight pressed in the position you want under a pile of books. Works like a charm.