The phrase but yet is almost always a redundancy. Either but or yet usually conveys the same meaning in fewer words. Consider this sentence:
The government can’t even supply our people with simple, ordinary flu vaccine, but yet they can run the health care system?
This has the same meaning, without the redundancy:
The government can’t even supply our people with simple, ordinary flu vaccine, but they can run the health care system?
And so does this:
The government can’t even supply our people with simple, ordinary flu vaccine, yet they can run the health care system?
