I can't seem to transfer a Terraria character and world to a flash drive
As Teo said here:
Actually I managed to find a way, I don't know if it'll be the same for you guys but it's basically go into your Library > Application Support > and there should be a folder in there called Terraria that has your worlds and players and servers etc
Another solution: If you are playing Terraria 1.3 on Steam: click the cloud icon on the bottom-left of the player/world card. After that, you can access it from any computer.