I used the flat wire in a previous install. THe wire is about as thick as a business card. So, while very, very, thin, it is still visible on the wall, on close inspection, even with a thick cost of paint on it.
However, a coat of spackle fixes that problem. The key, of course, is getting a nice blend from back into the wall. Sanding is necessary to get the spackle to blend smoothly. A cost of paint - and bingo, the wire literally disappears.
Not to c*ck block axiom, but the flat wire can be obtained for much cheaper than they sell it here. A google search should fix you right up. Nowadays, there are more than one company competing to sell the stuff, which is good.
Also, the "coupling" accessories that let you connect flat wire to regular round wire are a bit unnecessary, if you ask me. The flat wire can be crimped with a pair of needle nose pliers and stuffed right into the binding post or banana plug, or spade, etc.
What I did to save a little cash was to run regular round wire along the baseboard underneath a wire track placed just above the baseboard - which provided a nicely unobtrusive seem that looked very much just like an added bit on the baseboard. Many of the guests didn't realize that the wire track was even there. Then, at the wall base (mine was conveniently hidden by a couch, which meant a clean transition from teh baseboard to the wall was not as important), I simply crimped and electrical taped the round wire to the flat wire.
The look was that of in-wall wiring, without the added cost of tearing down dry-wall. Total installation time took about a days to do it right (including drying times).