Make sure you have SSH keys for Github setup so that you can do this from a command line on the build machine
git clone firstname.lastname@example.org:scottellis/private-repo.git
You should run that clone command at least once. If the github server keys are new you’ll need to answer the prompt from ssh to accept the new key. If this happens when running bitbake the process will hang on the fetch stage.
The SRC_URI to use in the bitbake recipe is