The issue was raised in early 90's. Since blue wavy line represent river Danube, it is hard to interpret it as green. The flag without the arms is also in use. The church was finally consecrated in 1905, and in 1931 it was awarded the title 'basilica minor' by the Holy See. The right hand of Stephen I, the first Hungarian king, the 'Holy Right', is preserved here in a shrine exposed in a side chapel close to the church entrance.
Flag has a golden fringe on the lower edge.
Looks like a typical procession banner. I am not so sure of the charge, since it was rather dark. The Holy Right is paraded by the faithful each 20st August, and I guess the three flags are involved in the ceremony. Historical informations are from the Budapest guide, released by the Tourism Office of Budapest.