Surely the royal family has had his dna tested in the 30 years since the rumors started; and if he were not Charles’ son, it would have been dealt with decades ago. Harry is dumb, but not a bastard.
I'm sure the DNA tests were done. If Charles is not the father the test results would remain a secret. No reason to have a scandal and make Diana's infidelity public.
Harry would have been told that he would never be king. Harry got so ticked off with the queen and the rest of the royals that he married a twice-married black divorcee. Then he connected with his friends the Clintons and Obamas to start a money making foundation.