I am looking for a way to cut out 1/16" squares of Kapton from a sheet of 0.002" Kapton film. I have had little luck finding a puch and die set for use with a bench top puch.
My first instinct would be to make a drawing of the punch and die needed using one that fit your existing punch press (I'm assuming that you have one). I would then take the drawing to a machine shop and discuss with them the application and tolerances needed for your application.
Of course my comments are just a shot in the dark since there is little information to go on. Perhaps others have better suggetions but even they would like to have more information.
Check with the manufacturer of your punching machine. If they don't
make a standard 1/16" punch and die set, they may make a special for
you. I'm not sure if you want to save the holes or the slugs. I will
tell you that Kapton has a nasty habit of propogating cracks from sharp
corners. If you want to use the part with the square holes, you should
be aware of that.
You may use waterjet or laser to cut almost anything. You could array several on a sheet with a small amount of material to keep the 1/16" pieces hanging in and clip them apart as you need them.
What will be the end use? Tolerances? How many squares?
Cheap and dirty, loose tolerances, (going with your "bench top punch") file down a penny nail to 1/16" square, use a piece of hard rubber or neoprene as a die - just a flat sheet - and you can knockout a few squares.
Or you can cut the .002" sheet into 1/16" strips and snip the lengths to 1/16" - but surely you have already considered this.
As a general rule, the volume, or quantity required will determine material selection, design and construction of a die and punch system; so in order to get a viable solution to your dilemna, it would be best to provide more information up front. - Less information = more off-the-wall responses.
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FRIENDS DON'T LET FRIENDS DRIVE HUMMERS
Do what Henry Ford would have done. Send your Kapton to the people who
make photographic film and tell them they can keep the Kapton if they
send you what they remove.