Hey Sam,
FME Flow version control was not made to be manage from a remote git.
Remote Git is only used when you need to back up your workspaces versions to be able to update your FME Flow without loosing them.
From the documentation :
Version control allows you to access previous versions of your Repositories files. Optionally, when you configure version control with a remote Git repository on GitHub, you can maintain backups of your versions outside of FME Flow. These backups are useful if you perform a backup and restore operation of your FME Flow (including as part of an upgrade), because version history is not maintained in the restored FME Flow.
Note that version control does not, by itself, enable you to update your local working copy of Repositories files. Instead, version control allows you to download previous versions. Once downloaded, you can update your working copy by republishing to FME Flow.
So, there’s no way to choose a branch, and I think you should not connect it to a remote for other purpose than for updating FME Flow.