Hello,
is it possible to move/rearrange the elements of a UV map once flattened with UV master?
Yes. You can do it using Move/Scale/Rotate mode and the Transpose line. You will need to mask out the islands you don’t want to move, or set Brush>Auto Masking>Mask By Polygroups to 100 if your islands are separate polygroups.
What you can’t do is scale the whole UVs within the grid (for example so that UVs for a different subtool would fit in the same UV space). UV Master automatically scales the UVs to best fit the grid when you press UnFlatten.
If the map is grouped, you can select individual groups to move or scale by holding Shift+Crrl and clicking on a group.