I've done this a lot of times for various customers. You have to go to the hardware store and get these little aluminum
" T- screws " You know, the ones with two parts that screw together. you can get different thicknesses, so measure how thick two pieces of plexi (plus a flag) are, and get that thickness. You can cut them down with a hacksaw and make them the right thickness too. Drill your holes around your plexi. clamp down the two pieces of plexi, and drill through both layers. careful not to have the plexi pop up and crack.
After all your holes are pre-drilled and lined up with each other, position the flag. figure out a way to make it stick to the one sheet of glass. Either use dabs of white glue, or tiny bits of double sided tape. I'm not sure how concerned they are with conservation, but these ways work, and you don't need much to make it stick. There is a tape used in the film industry called "Super Tape" it's very strong double sided tape. I imagine this would quite well, if you can find it. It comes in light blue paper rolls. The glue is like really thick AGT tape.
if you don't want to use glue, I imagine you could position the flag, and drill tiny holes where you want support. Then sew the flag through the plexi. I haven't done this, but could be an option.
After the flag is stuck, put the top piece of plexi on, line up the holes, and tighten the T screws. As far as hanging... either drill holes in the corners, and at the center of each side, and have the client drill the pice to the wall, or attach two D-rings at the top corners, and hang it that way.
I don't know if this all sounds crazy, but if you can do it well, the customer should be happy.
Those items that K Allen described are called binder posts. They are from a previous generation when invoices and paper would be punched and put in binders. The posts were to hold various thicknesses of paper together between two covers. The binder posts come in a variety of lengths and are all hole punch diameter. If my memory serves me correctly, they came in sizes from about 3/4" to 3" long.
A good stationery store should have them but do not expect to find them in a big box stationery store. There are numerous ways they can be used in framing with a little imagination.
If you want to see them go to this site and click on any size to see what they look like.