Despite having only earned eight caps for England, Sinckler has been picked by Lions coach Warren Gatland for the tour to New Zealand, which gets under way on June 3.
Sinckler has paid tribute to fellow Harlequins prop Jones for his effect on his career.
He told BBC Sport: "Looking back now, when you are a young player, you want to play. Then you see Adam Jones come into the club, and you are probably not going to play as much.
"From my first day, Adam has been unreal. He's been like a coach to me, even though he is a player.
"He will be a top coach in no time at all. He's been a coach, a mentor, a father figure to me - and a headmaster when he is telling me off."
Jones toured South Africa in 2009 and Australia in 2013 with the Lions.