If I have a Flow with independent time signatures in a multi-flow score, using w to jump to the Part does select the music in that part, but always scrolls to the beginning of the first flow.
here’s the score with almost all of the notes removed, try it with the piano part in the very end measures of Flow 3.
I think we will need to see the project itself to provide any insight here. Provided the same flows are present in both the full score layout and the part layout, it should work as expected.