I'm not a doctor, but do have too much experience with kidney stones
. For me, I'd get pings and pangs in my kidney
as well as microhematuria (blood you cannot see by eye) in my urine when I have stones. I've also had the flank pain you describe .. for me it's been in the lower back. I hope with lots of water your stones move out for you uneveventfully.
Please keep in touch. From what I've read stones <5.0mm usually move out on their own with a high % of non-complications, etc.