I find that most striker pneumatics are made of 3/16" thick poplar
(a.k.a. "whitewood").  This material, nicely planed to uniform
thickness, is available at hobby shops or most any factory that makes
wooden rulers.  Home Depot and Lowe's now can supply a wide variety
of nicely prepared whitewood (and mahogany, maple, oak, etc.), from
quarter-inch thickness upward -- just about anything you would need to
build a complete stack from scratch.

For pneumatics, the wood needs to be cut burn-free with a hollow ground
blade and good bearings on your table saw.  It is essential to size the
end grain with a preliminary coat of glue that is allowed to dry before
covering.

I have gotten away from using cloth for hinges, preferring instead to
use round punchings of medium-thickness fairly stiff leather.  Prior to
installation these are folded and then creased with an electric iron on
low heat.  And I still _always_ use hot glue with any cotton-backed
covering material.  (Note: Sorry, I am retired and no longer do this
work commercially.)

Jeffrey R. Wood