That would crush the stitches. I've seen bookmarks in plastic sleeves, but vinyl is active, & would eventually migrate into the cloth. Other plastics might work, if you could stitch the bookmark inside a rectangle with narrow borders.

Jlhewes is right the stitches would be crushed if you laminated them. I have made many bookmarks and put fusible interfacing on the back to protect the stitches and they have been just fine for years. I have one in my Bible that I have used for 20 years and it still looks fresh.

If you really want them protected (my son would have soiled one even in his Bible...just that kinda guy), I agree that laminating would crush the stitches. I've gotten sleeves from scrapbook vendors that are acid-free and you could perhaps alter one for a bookmark. I'd just sew up the sides of the acid-free sleeve. I would use my sewing machine, but you could do it by hand. I wouldn't use my expensive fancy machine, but only because I know that I can sew anything on my old treadle. As long as it fits between the foot and the pressure plate...like, oh, uh, leather, soft think plastics, vinyl, upholstery fabrics and well, my fingers...more than one at a time. My kids used to tell each other not to pester mama if they heard that wheel was humming!