How do I make a rideable flying mob move faster?

Make a procedure that runs on the entity's update tick. Then, use an 'attempt to override motion' function to set the entity's x/y/z velocities to the entity's x/y/z look angle vectors. This will make the entity move at a constant rate in the direction it's looking. You can then multiply the look angle vectors to increase the speed as much as you like.

Hello do have an example MinedThemoods?

Screenshoted? I just sucess for veritcal mouvement