How should I run wiring for my above-fireplace mounted TV?
I agree with @DA01 that it'll basically be impossible to fish horizontally through studs and insulation, without having to cut open all of the sheetrock. Then you have to deal with sealing it all back up air-tight, and patching the drywall and repainting (at least the entire wall, and maybe the entire room, depending the paint match). 

So a couple alternatives:



Use a wiremold type product to surface mount the conduit:



There are lots of different brands, and it can be paintable. With planning, you can minimize where you see it.



Build up the wall using cabinets or a false wall, so you can run wire in behind, on top of the existing wall. 

Could be as simple as just a drywall section sticking out, or some built-in cabinets or some brick work. Cabinets of course have the benefit of being able to build in other components such as your A/V gear and speakers.