Monopoly (advanced) with speed die
According to the rulebook, you get out of the Jail if...


  (2) 
  using 
  the 
  "Get 
  Out 
  of 
  Jail 
  Free" 
  card 
  if 
  you 
  have 
  it; 
  (3) 
  purchasing 
  the 
  "Get 
  Out 
  of 
  Jail 
  Free" 
  card 
  from another 
  player and 
  playing 
  it; 


Regarding the speed die:


  Use 
  the 
  white 
  dice 
  ONLY 
  when rolling 
  to 
  get 
  out 
  of 
  jail. 


Therefore, if you play the "get of of jail free" card, you immediately get out of jail and you roll to move, not to get out of the jail. Therefore, you do use your speed die, as you're already out.

Nevertheless, if you roll to get out of jail and you roll doubles, you still do not use the speed die, even if you succeed. It's just that when rolling to get out of jail, if you roll doubles you use that result as your move.