Unfortunately KioskBuddy KDS currently only sees kiosk orders, so it won't see things Square Online and Square POS orders. However, while we meant for KioskBuddy KDS to be a backup for those without an existing KDS system, this is a frequently requested feature that's high on our product roadmap. We plan on enhancing KioskBuddy KDS to see all orders on the Square platform. If you're interested in beta testing this new feature, send us an email to support@kioskbuddy.app letting us know!
In the meantime, as a workaround you might consider using Square KDS, which is supported with this new feature.