Snyk does support Gems hosted in private GitHub repositories by default.
You can contact firstname.lastname@example.org to have this feature enabled for your organization.
After this feature has been enabled you can define Bundler environment variables in your organization or project settings.
Note that this will only work for gems over HTTPS such as:
gem "privvy", git: "<https://github.com/user/ruby-gem-for-private-source>"