"I'll see you on the flip side" usually means "Until we meet again" when two people have the intent of seeing each other again soon. In context, if the father and son are on an adventure and they need to temporarily split up, this is a phrase that could be used. It would not be used as a standard 'goodbye' unless you're leaving with the intent of meeting up with them again within a relatively short period of time.
Hope this helps!
(اسف، انا اتکلم العربیة جيدا.)