Not at a machine to try it out, but how about creating a cross section in the flat pattern parts, at half sheetmetal thickness say, then create datum curve from X-Sec and create an analysis feature referencing the curve feature in it's entirity. You should then have a parameter LENGTH in each, stick 'em on a drawing use Pro/Report to sum them.
or, and this is hoping... ... ... stick ALL your flat patterns in an assembly on the same horizontal plane but not touching on another. Create an assembly level cross-section, create a datum curve from X-Sec at assembly level.
Stick an anaysis feature on THAT curve and have the whole perimeter of all of them????
That may be wishful thinking, although if it does work you'd just add in a new bits and it would update the perimeter
