Question

How is the number of electric field lines emerging out of a conductor equal to flux?

Answer 1

It's not.

If you want a pictorial definition of flux in terms of field lines, then the definition could be "the number of electric field lines emerging out of a conductor", (`bb1`) perpendicular to the conductor's surface, (`bb2`) per unit surface area of the conductor.

The field lines are more properly called flux lines. The closer they are drawn together, the stronger the field