Yes, flint can chip, it can fly into your eye, and no matter how 'hard' it may hit, it is like a tiny shard of Glass, it Will do damage.
I had just mounted a new French Flint last month, the first shot I was struck in my right eye - But I was wearing glasses - it hit hard enough that I heard it as well as felt it. I don't recall this ever happening before. When I checked the flint there was a decent sized chip off the Bottom of the flint right in the center.
As for standing on the right of a flintlock: for expodition shooting we were always told to have a No one on your right, we were to always stagger ourselves...well, will doing a show on a pier one guy got excited (we were shooting blank loads at a ship sailing by) he did not wait for my line to step back before moving up with his line and he reached over my left shoulder with his pistol and Fired - the Flash Burn to my face (luckily nothing to my eye) Hurt Like Heck! And it's like a Real Bad Sun Burn, the sting and pain lingers long - ya, I went off on him, he thought I was a jerk, I dont care, it HURT LIKE HECK, IT BURNED, IT STUNG and that was Too Close to my Eye!