This page lists all of the relationships that Bad Jack's Son shares with various characters throughout the series.
Jimmy and Bad Jack's Son share a pretty good friendship. When Jimmy wants a new helmet to replace his old helmet, he calls up Bad Jack's Son for any spare helmets. Bad Jack's Son decides to go through his father's treasure, despite the possible upcoming consequences for a new helmet for Jimmy. After he gives it to Jimmy, he considers Bad Jack's Son a best friend. In Treasure Trap, he and Jimmy are shown to have a close bond, despite both their parent's unapproval that humans should be friends with dragons.
Bjorn and his father seem to share a fair father-son relationship. In Epic Ballroom, Bad Jack is seen playing ping-pong with his son. In other episodes, Bjorn seems to be minorly annoyed of his father's anger and him going out all the time. In Treasure Trap, Bjorn and Bad Jack are seen in a castle, trying to find treasure.