How can we relate the idea of flux with electric field Doesn't flux mean the measure of flow of something  represented by vector A. But in the case of an electric field we have nothing that actually flows . So how can we use the idea of flux while dealing with electric fields
 A: Doesn't flux mean the measure of flow of something represented by vector A. But in the case of an electric field we have nothing that actually flows . So how can we use the idea of flux while dealing with electric fields
Actually you can think of electric flux as something that flows. It represents the flow of the electric field across a surface. You can also think of it as the flow of electric charge placed in the field. A positive charge placed at rest in the electric field will move along the path of the electric field line. 
The electric flux through an area is defined as the electric field multiplied by the area of the surface projected in a plane perpendicular to the field. An electric field is defined as the electric force per unit charge. The direction of the field is the direction of the force that a positive charge would experience if placed in the field. 
Now look at the electric field patterns that @tom showed you in his answer. Envision placing a positive electric charge at rest into the field. That charge would experience a force in the direction of the field lines, causing the charge to move ("flow") in the direction of the field lines. The denser the field lines, the more force the charge experiences causing it to accelerate more and go faster. So you can think of those charges as "flowing" in the electric field. 
Hope this helps.
A: We can draw 'field lines' from positive to negative charges. These lines repel each other and naturally get packed in tightly together near point charges. 
See diagram for example here I copy one of the diagrams below...

Now to answer your question the idea of flux is about field lines per unit area perpendicular to the direction of the field lines. 
So where the field lines are tightly packed together the flux is high and the electric field strength is high
When the field lines are far apart the flux is lower and the electric field is weaker.
Note in the diagrams above the magnitude of the charge on the right hand side is always higher except in the case of the diagram on the bottom right. The number of field lines entering or leaving a charge is proportional to the magnitude of the charge. 
Sorry this is not a very mathematically rigourous answer, but I hope it explains how the idea of flus fits with electric field. 
A: 
How can we relate the idea of flux with electric field

I don't think you should. I think it causes confusion.   

Doesn't flux mean the measure of flow of something represented by vector A. But in the case of an electric field we have nothing that actually flows. So how can we use the idea of flux while dealing with electric fields

Well said. Note how Bob said "You can also think of it as the flow of electric charge placed in the field". That's fair enough. The lines represent the motion of a charged particle placed down somewhere. But note how tom put "field lines" in quotes? They're sometimes called lines of force, and the reason why is important. 
Maxwell unified electricity and magnetism. The field we're dealing with is really the electromagnetic field. See Wikipedia: “over time, it was realized that the electric and magnetic fields are better thought of as two parts of a greater whole – the electromagnetic field”. You can also read what Jefimenko said: “neither Maxwell’s equations nor their solutions indicate an existence of causal links between electric and magnetic fields. Therefore, we must conclude that an electromagnetic field is a dual entity”. See what  Jackson said: “one should properly speak of the electromagnetic field Fμv rather than E or B separately”.
Electromagnetic field interactions result in linear and rotational force. When we contrive our charged particles such that linear forces cancel out but the rotational forces don't, we say we have a magnetic field. When we contrive our charged particles such that the rotational forces cancel out but the linear forces don't, we say we have an electric field. You can call it a vector field because there's a magnitude and direction at every point. But this electric field isn't a field like the electromagnetic field is a field. It's just a region where a particle with an electromagnetic field will move in a linear way if you place it down with no initial motion. Because of other charged particles with other electromagnetic fields. However if you throw your charged particle through the region, your particle will exhibit rotational motion too.  
So those lines are really lines of linear force, not field lines. So there is no real electric flux in terms of any kind of flow. That's why the Wikipedia article says "electric flux is the measure of the distribution of the electric field through a given surface,[1] although an electric field in itself cannot flow". And that's why you should be wary of sources and sinks in an electromagnetic context.   
