After some research, I settled on the ASMT-UGB5 series green LED from Avago Technologies. They’re small at 3.2mm x 2.8mm and give out a whopping 1,800 mcd, or millicandelas. I designed a grid on a 50mm x 50mm board that I would cut out into separate pieces. Each LED needed its own resistor. In total, for 22 flags, that ended up being 264 LEDs pared with 264 resistors.
Here’s a short video of the assembly and cutting process: