Looks like silicified limestone/dolomite. The better grades of it will knap, and you're right, wood is the best thing for it. It's really variable-one rock may knap good and the one lying next to it won't. The better stuff is good for large percussion pieces, but you're not going to get nice pressure-flaked arrowheads out of it unless you find some really highly silicified stuff like the Alibates stuff in Texas. I find some in Eastern TN that works pretty good. If you have limestone/dolomite, you probably have chert outcrops somewhere in the area.