DL,
this site has the dimensions of different size flags when folded. It says a 3x5 is 13-1/2 on the hupotenuse so that’s similar to what you got. It’s the only reference I could find for a 4x6 flag so I had to go with it and hope for the best.
I did ask him about cloth or Walnut and he said he “thinks” Walnut so I’m giving both options on the same insert. I didn’t ask about color, just assumed black but that’s a good point. I’ll ask him what color felt to use.