The rules say that the "complete adventure must be fully playable on one single sheet".
Is it allowed for jam gamebooks to have supplementary tools? I.e. ask player to get a dice, poker card deck, pen and pencil etc., so they can roll dice(s), do something with cards, or draw something when game instructs to do so?

YEAH! Your game can make use of dice, jenga, playing cards, tarot, whatever you want to use to aid the mechanics of your game.