The only practical reliable solution last I checked to syncing on iOS is to go with their paid service or use iCloud and set up iCloud on the desktops you want to sync with. You can jump through hoops with GitHub sync and a paid GitHub client on iOS that makes syncing fairly easy but fundamentally iOS does not really allow background syncing for anything but iCloud. There was also a selfhosted syncing plugin I tried out before that may have gotten better but I just found it too unreliable. Worth checking out perhaps.