I was reading the card Chains of Mephistopheles and I found these great flow charts for how it's replacement effect works. Would I be allowed to bring a simple flow chart like that to a sanctioned event? Would this change if the event was Competitive or Professional REL?
No, you cannot refer to pre-made notes or diagrams like that during matches in a tournament. The Magic Tournament Rules section 2.11 says the following:
Players are allowed to take written notes during a match and may refer to those notes while that match is in progress. At the beginning of a match, each player’s note sheet must be empty and must remain visible throughout the match. Players do not have to explain or reveal notes to other players. Judges may ask to see a player’s notes and/or request that the player explain their notes.
Players may not refer to other notes, including notes from previous matches, during games.