How does the Magnetic field and Magnetic flux through a multiple-layered solenoid depend on the number of layers?

The magnetic field inside an infinite (very long) solenoid depends of the current intensity and the density of wires of the solenoid:

$ B = mu_0nI$

for a solenoid in free space. $n$ is the density of wires. As you can see, $B$ is constant everywhere inside and the field is 0 outside the solenoid. So if you stack multiple solenoids, the fields adds up together and the resulting value will depend of where you look; if it is inside the central solenoid or between two consecutive solenoid. In either case, the field will only depend of solenoids external to this point since the field is 0 outside of a solenoid. When current flows in the other direction than another solenoid, the field takes up a negative value compared to the first solenoid so field can cancel up and it only take at least two solenoid to cancel a field (there can be more and it does not need to be an even number).