As far as I can tell, the wikipedia section you refer to says nothing about flipping.
It only says that up has a certain probability and down has a certain probability and it shows what the bra-ket notation for this is.
Furthermore it says that once you measure it, the probability collapses.
It doesn't say to which state it collapses nor from which state it came from.
Nor does it refer to the Stern-Gerlach experiment.