This is going to depend on the multi-factor authentication software you use.
Some sync to the cloud, so you can just sign into the software on the new phone and it will sync up.
Some back a backup/restore option, so you run backup on the old phone, and then restore the backup on the new phone.
For example, Google Authenticator supports both doing backups and syncing.
In the worst case, un-enroll your old phone, and enroll you new phone.
