John Constantine can use magic despite the fact that he is supposed to be punished for allowing another Flashpoint to happen. It would be unlikely, as magic is John's main weapon and could lead him out The House Of Mystery, Spectre would not have allowed this and would have blocked these abilities.
Animation error: When Constantine is playing cards he has what is called the Dead man's hand but the two cards are shown to be a red club and red spade instead of hearts or diamonds.