I had a look at your shapes and these are more complex than I know how to deal with. It looks like you have used a dynamic line connector which autoroutes - even moving one of the original segments causes the original connector to reconfigure so that automation is what is causing your problems.
I fiddled with the shapesheet a bit to see if there was a magic setting but nothing seemed to work for me so that was a deadend.
My suggestion is to either:
- export your drawing to a different format (eg .png or .emf) and then import that back in to your drawing and flip it.
or
- ask your question on another forum where the real Visio experts hang out (and include links to any other locations where you ask the question). Maybe this one
Visio Guy - Index
EDIT: I see you have already asked the question on that forum and wapperdude's advice works for me on the file you posted. Flip the flow chart