Is the batter credited with a double if he is thrown out while advancing to third base?

No, once you are tagged out you don't get credited with anything if you are the one at bat. Now if another batter hits the ball and there was already a man on base at first and he gets tagged at 2nd base, then yes the man on 1st base would get the single from his previous at bat If the batted ball was cleanly a base hit and he was thrown out trying to advance past first base then the batter would be given the hit corresponding to the last base the batter reached safely. If the batter was thrown out at second, the batter would be given a single. If the batter was thrown out at third, the batter would be given a double. If the batter was thrown out at home plate, the batter would be given a triple.