If you want the behaviour that you seem to be describing then the flow boxes should be two objects, not one object with two paths. This is demonstrated by examples/flowsample.svg and does work.
Impressive, but forgive me: how can I edit this on canvas? I can only edit one object and don't understand, where the rest of the text is flowed into and how the flowing around that hole is achieved...
Select text tool, click in content, start typing...? That works for me. If you wanted to move the regions that's actually not so easy because that file was constructed by hand and doesn't conform to the way Inkscape likes to do things (the regions are repeated: once visibly and once for the flowRegion, so if you try to move them you only move the visible one. If Inkscape had created the document it would have used a <use> tag to share the same shape for both).
In order to create one yourself you will need two shapes (separate objects) and some unflowed text. Select all three and do Text->Flow into frame. The order in which the frames are used depends on the order in which you selected them, so if it's wrong hit undo and try again.
The hole in the middle of flowsample.svg is done with a flowRegionExclude tag, but there's no need for that (and, in fact, no UI for it either) - you can just create a compound shape using, for example, Path->Difference.
It is a bug, please file it as such.
[ 1816130 ] Wrong behaviour of text flowed into a combined shape
Thanks.
Richard.