Since there is *no* monopole in Nature, we *cannot* assume that *field lines* start *at some* infinity and end *at* individual charges. In fact, lines start from *one* charge and *travel to infinity* and then come back to the *other* charge. 

Since flux is defined as *integrated electric field over a surface,* you can enclose your charges with *identical* (Gaussian) surfaces and attempt to calculate the integral. By *Gauss's law,* however, this integral is proportional to the *enclosed* charge. Then, it is trivial to see why bigger charge contains *more* flux than the smaller charge.