I believe that the first head of state to fly in an aeroplane was King Ferdinand of Bulgaria on a visit to France in 1910.
According to the Royal Family's website, George VI (then just Prince Albert) was a member of the RAF between 1918 and 1919 and the first to fly (he gained his wings, apparently), followed by Edward VIII (then Prince of Wales) in 1929 - he took a trip in a Bristol Fighter, followed by Prince George (later Duke of Kent). They both learned to fly as well. I dimly recall seeing something about Edward partcipating in one of the Air Defence exercises in the 1930s. He was also the first reigning monarch to fly, since he established the King's Flight in 1936.