Rabbits don't like being flipped over, because it exposes their most vital organs. BUT! Every single rabbit can be flipped, and should be used to it. Just like a baby doesn't like getting their diaper changed, there are some things that rabbits need to learn for their own good. There are quite a few videos on YouTube about how to flip your bunny over. You basically get a good grasp at the base of their ears, getting a bit of their "scruff"...then take your opposite hand and support their back end as you flip them over. Make sure you rest their weight on a solid surface. When they are flipped over correctly, there's no stress or struggle. Once you flip, make sure to keep your "ear" arm resting alongside their body, for added security for the bun. With practice it'll both become "old hat" to you both...and they'll realize it's not a big deal.
When a rabbit is flipped over, it's so easy to check their teeth (which everyone should do at least weekly), any moisture under their jaw (signs of tooth trouble, abscess, etc), inspect all their nails (checking for missing/broken ones), get a good look at the inside of their legs (for snuffles, etc), feel their abdomen (for any abscesses, lumps, injuries), check their penis/vent area (checking out scent glands, signs of scabs, redness, etc), their hocks and back toenails, etc. This should be done at least weekly and only takes a minute or two to inspect everything and make sure there aren't any problems creeping up that would otherwise go undetected until they were blatantly obvious when they're upright.