It's around 28" give or take a few inches. You can crawl under it on your hands and knees. They have dug out holes under there from dust bathing so it does vary.
My suggestion for the 4'x6' coop is to have your underneath access door on the 6 foot side and make it plenty wide or even have two doors. Just keep in mind you may have to crawl under there sometime. Height wise I would agree 30" would be more than enough for the chickens.
Before this fall I plan on making a full height door in the front under the white door. I had also thought of doing most of the caged area under the coop solid walls for winter. Would be easier to keep drafts out in winter and give the girls more sheltered space.