Most embroidery shops can do that work.
Some will choose not to embroider on vinyl because the perforations are so close together that under stress, the vinyl can tear along the edge of the sewing, almost like tearing a check out of your checkbook. I have only found two places in Des Moines that will embroider on vinyl, and one of those required a sample piece of vinyl to work on first. The other wanted to "laminate" another backing on the vinyl across the whole width so that it would help prevent the stress tear.
To get it done, you need a vector file, and you need an experienced upholsterer who can tell you approximately how many stitches you'll need to make it look right. Too few stitches & they become very long, trying to fill the space with color and easy to snag; too many and the stretchable part of the vinyl makes it start to lose shape and pucker. The vector files are not terribly difficult. Any of the t-shirts or other graphics I have done are available as a vector file. Since you pick your thread, it doesn't matter what colors are used in your digital version - you could bring him something in various shades of hot pink - as long as you can identify which color thread will be used for each variation, it should turn out great.
