Is it legal to make a non-military stealth plane?
Yes you may, but you need to carry a mode C transponder while above 10,000 ft or in some types of controlled airspace and have it switched on. Which pretty much negates the stealth capabilities of your aircraft.

To quote the linked AOPA page:


  According to 14 CFR 99.13, no person may operate an aircraft into or
  out of the United States, or into, within, or across an ADIZ
  designated in subpart B unless operating a transponder with Mode C.
  Certain exemptions might apply to aircraft that were not originally
  certified with an engine-driven electrical system; see 99.13(d).