I usually install the foot rest bar about 8" to 10" off the floor.

Best bet....to be comfortable for yourself, sit in the chair, and put someting on the floor, like pieces of 2 x 4, or jars, or buckets, anything, so that the height feels comfortable for you. Now..just measure that height off the floor, and that's where you place the foot rest!

I could be way off base here, but I believe they're not actually foot rests. Just spacers between the two legs to keep them from shifting when one sits down on it to prevent the legs from giving way under the weight. I have a dining room set with a chair that's missing one of those, and the two legs that were connected to it spread out when someone sits down in it.

If there's any kind of standard that's attached that determines how far down they need to be, I would assume it's based on where the legs will take the greatest amount of pressure when weight is applied; the most-likely "snap point" at which the legs could snap. I would say the height of the chair is the determining factor, but smack in the middle (between the seat and the floor) is where I've seen most of them.