What does "quartermaster officers should be filled by detail from the line"?

quartermasters are the folks in charge of making sure that supplies are ordered, received, and distributed to the rest of the army. "detail" means to order a group of people to a task, like a work detail or a patrol. The line means the part of the army that is at the front, usually. Not the reserves, and not headquarters staff and support, but the line, the active duty folks, the people doing the actual primary task of the army (being ready to fight, perhaps even actually fighting).