Thank you everyone for the ideas. I will let you know how it turns out.

I'd recommend a product called "Restoration", made specifically for vintage textiles. Soak the top, do not agitate. If you do it in the washing machine, you can spin out the water, then add rinse water (again, no agitation), soak that for awhile, spin it out. Then repeat with another rinse the same way. Do not put in to the dryer. The best way to dry is to lay flat (outdoors in the shade ontop of a clean sheet, indoors the same way if you have the space--if not hang over a clean clothesline in the basement). I believe the red fabric shown is much older than you think. I think it's from the 1800's, possibly a Garibaldi print.