It seems many sports have a system but it isn’t always followed. It may start with team owners and then voting to push it forward or ‘commissioner’ role may just implement something arbitrarily, something where it follows a convoluted path where other sports have a very rigid and set path for a rule change proposal.
It generally depends on what the rule is and how urgent it is to enforce. Generally, someone brings up the idea (whether it’s the players, owners, or coaches). It is then discussed by a committee of owners. Once approved by them, it goes to baseball’s playing rules committee for approval, which is made up of different execs. From there it can be put into effect, although some have to then be run by the MLB Players Association (the players union) for approval. It generally depends on the nature of the rule and who it will effect, though.
For an example, look here. That will give you a small sample of what happened this year when they tried to change the strike zone.