I started with brass pan primers with 3grn plunger dispensers, and have switched to an antler pocker primer and a horn pocker primer. Either will fit into the pocket of a hunting shirt, and both have the same 3grn plunger dispenser tip as I like the consistency & convenience. They each also have a small brass threaded filler base plug.
Also, since I refresh my prime at least once an hour when sitting on a deer stand, it takes very, very little movement to slip the primer out of a shirt pocket and dispense a fresh charge in the pan.
'Flat' horns are made usually by boiling or heating the horn piece in some way during the process, and when soft are gently pressed to change the full round shape to a flatter appearance while they cool and harden.
"John" at October Country made mine, does excellent horn work at very reasonable costs...(octobercountry.com)