Would there be a magnetic null point of a flat coil when pulsed dc is passed through it?
I'm puzzled that you think it 'should'.

Consider all the current elements that make up the coil. Use the 'right hand rule' (google or wikipedia, or both) to understand the direction of field in the middle of the coil that each element generates. Then notice that they all add up rather than cancel.



It doesn't matter what angle round the coil they are, or what radius, all the axial components of field from the circumferential currents will add up in the middle of the coil. It doesn't matter whether the sides are round as shown, or straight as in a square coil, the circumferential component of the current will generate the central field. All that matters is that the current goes 'round' the axis. It doesn't matter how many times it goes round, once or a hundred times, or any integer N.