On farm we bought 7FT poles, at 48" to get below frost line gave us 5 ' average height in the poles, the wire started about 6" below top. Barb wire fences don't need a 6 foot height and never seen that height. Be sure the wires are on the inside of what you want to pen or keep from going through. For cattle we usually had 2 strands, but if smaller animals, goats, etc. we would have 3 strands.
Horse owner very rarely would use barb wire fences, in fact we never pastured our horses in a barb wire pasture. Rarely ever saw a barb wire fence above 5 feet. Hope that helps.
OOps. my error. I see you want barb wire on top of a chain link fence. I have one in back yard separating my land from a preserve. The fence is 6' and the barb wire are 2 strands angled outward at a 45 degree angle added top to fence post. Sorry for error.