Can you use masonry paint on patio flags?

You can but it wont stay down very long. Masonary paint,both water based and oil based are for exteria decoration and to a degree protection against weathering. They are for walls. Any walk way will have wear on it caused by the traffic which will quickly remove the masonary paint. There are readily available pints for flooring internal and external. They are expensive but are created for the role of flooring coverage and the traffic abuse it will take.