I've usually thought of the signal flags as being stored in a cubby hole style cabinet with a small space for each letter. That allows quick retrieval of the correct letter without having to unfurl it first.
I think charts were stored in wide, deep, shallow drawers the same as in a drawing office. They make it easy to thumb through to the correct chart without beating them up. It is also easy to slide a chart back in at its correct position in the stack. If you have a lot of charts a stack of these drawers becomes a cabinet that you can use as desk space for reading the charts.