Clearly the idea has worked in Russia, but I find it hard to see how charging a flat rate can be financially viable. The pricing seems like such a fine line to make it cheap enough for its intended usage (people hanging around and such) but expensive enough to cover the food. As other commenters pointed out already, you could walk in, take a bunch of food and expensive coffee and leave.
I think one way of attacking this problem would be similar to taxi-cab pricing (X for the first mile and Y (where Y<<X) for every subseqeunt one. Essentially adding a flat fee of a few bucks just for walking in, then charging a small amount per minute to hang around.
They don't offer food (bring your own) just cookies, and you won't realistically chew too many cookies. They also have coffee from coffee machine. The whole idea is to make it feel like home (that many people in the city lack while renting something ugly) - assorted old furniture and a good company.
I think one way of attacking this problem would be similar to taxi-cab pricing (X for the first mile and Y (where Y<<X) for every subseqeunt one. Essentially adding a flat fee of a few bucks just for walking in, then charging a small amount per minute to hang around.