Before starting off with your planned flag case making, one important thing to take note is to know the size of the flag that would be placed in it. There is no sense of having an under or oversized case since it would simply not look good altogether.
As a start, let us suppose that the flag to be used would be a burial flag which measures 5 feet wide by 9 feet long. You would have to start off with one measurement to go horizontal, and a couple for the diagonal. Another dimension to measure would be the thickness of the flag when it is folded.
Next, determine the material to be used. Let us consider using mahogany for this one. With the dimensions in mind, and the material at hand, it would be wise to leave an extra one fourth or one half inch bigger than the actual dimensions when cutting the wood for the flag case. This is to ensure a little leg room for fixtures such as hinges, latches, or glass panels which may be inserted between.
With the angle board, it would be wise to use cutting equipment such as a framing square. Cut the base of the flag case and then set aside for later use. The other length side of the board must have the short point, wherein you must convert it into a long point by turning it around and cutting it off. This is quite crucial since by turning it around before cutting the other side, you would be having the two cut outs face each other later on with the same grain orientation.
Just add some minor fixtures and attachments to the two panels, and then you have your custom made flag case.