Does Coiling Wire Increase Resistance?

The simple answer is no. Winding wire on a non-ferrous form will not change its resistance. Of course, it all depends on the details. If the wire is uninsulated, and the form is conductive (copper, silver, gold, platinum, etc) the form will short out the wire turns and reduce the total resistance.

What does coiling a wire do?

A wire coil is an electrical conductor with one or more turns designed to produce a magnetic field. This is commonly used to increase the strength of a magnetic field. The more turns of wire on the coil, the stronger the magnetic field will be.

Why does coiling a wire increase current flow?

As the number of coils are increased the magnetic field will become stronger, because each coil has its own magnetic field, so the more coils there are the more field lines there are which means it would be a stronger electromagnet.