I'm wondering if you could just find some clear plastic or frosted plastic placemats from the 99 cent store? You could encase the fabric in two placemats with spray adhesive on the back of the fabric. Then clear glue to glue the edge all the way around the placemat.

Or you could just spray adhesive on a cheap plastic mat and lay material down and fold the edges underneath and glue. Then spray fabric with waterproofing spray.

Here is how someone else did it. See if it helps.

I guess as an alternative, you could try stiffening fabric with spray starch and then running it through the laminater. I've never laminated anthing so I'm not sure hoe stiff the fabric would need to be.

Good Luck!

Here is a link that might be useful: Placemats

You can buy iron on laminating stuff. It works for fabric or paper. It is easy to use and comes out great.
You can use your laminator for fabric, it isn't any different than laminating paper.

Big laminating companies will laminate fabric for people. There are web sites, mostly people who make childrens items for sale, where people coordinate to get enough material together to do a run which I believe is 50 yards. It can be many lengths of different fabrics as long as it is sewn togehter to make 50 yards of the same width. I considered joining in on one once which is how I know.
Maybe not useful to anyone here to know this but you never know!
kathy

Can you also use this type of iron-on laminate to stiffen fabric for jewelery making?