Pete,  Although I've not seen them all(!), I've seen quite a few Roller
Organs, and suspect that your organ had been rebuilt before.  All those
I've seen which I deemed "original" used leather flaps, both inside and
out, and those flaps were attached with a single dab of glue at each
end of the flaps, not tacks.

I've seen "modifications" that included everything from metal
reinforcement strips, wire holders, springs, thumbtacks, and materials
ranging from cardboard to Naugahyde.  I'd wager that the original
design with plain leather would work best, and allow air to escape
properly, too; you shouldn't need reinforcements.

Take a look at the wood at each end of the flaps, and see if there is
evidence of original glue.  (Of course it's quite possible that yours
is different -- is it of exceptionally early or late manufacture?  Even
then, I'd go with leather.)

Todd Augsburger - Roller Organs
http://www.rollerorgans.com/

 [ Naugahyde(R) is a trademark owned by Uniroyal Technology
 [ Corporation for their vinyl coated fabric product.  See
 [ http://www.naugahyde.com/index.htm & http://www.nauga.com/index.html
 [ -- Robbie