Two things.

1. The 3.5 mile figure is for resolving the stripes on the flag, not for seeing the flag. If you just want to see the flag, an aperture diameter of around 400 m is required.

2. The "Dawes Limit" is just presented with no explanation. It ultimately comes from the fact that the achievable angular resolution of an aperture of size D, using light with wavelength lambda is lambda/D. So if you were willing to work at 10 nm, then the aperture size goes down by a factor of 50 (of course working at 10 nm has it's own set of problems).