I don't get this magnetic flux concept?

To be honest, I have no idea what you were talking about in your first paragraph. I don't know what B is or what you mean by flux per flux per area. I think you are simply misunderstanding the notion of Flux. There is no multiplication. Flux is defined as a unit per area. Technically force per area is a flux, but it's generally just thought of as a pressure. A better example if energy received from the sun. The sun puts out light which is measured in Joules per second (or also just Watts). Then here on earth we receive that energy and we can calculate the amount of watts hitting a square meter of the earth. That is a flux. It is simply Watts per meter squared. Whatever your source is, it is either wrong or you are misunderstanding. As for you example of magnetic field lines, that is simple to visualize. Magnetic flux is just the number of field lines entering a unit area (it's a bit more complicated than that because there are no field lines in real life). That's all it is. Nothing with flux density times area or anything like that. Just remember, flux is a unit per area. It's easy to visualize it and it's simple.