Magnetically driven inertial confinement fusion targets have produced more than 1 GJ fusion yields in simulations, but azimuthally correlated magneto-Rayleigh-Taylor instability structures grow rapidly, degrading confinement and limiting performance. Axially magnetized, magnetically driven targets like magnetized liner inertial fusion develop helical instability structures, which grow less rapidly, providing enhanced stability; however, the origin of the helical structures is not well understood as the angles of the observed instability structures (~10º) are inconsistent with the ratio of the applied axial magnetic field (~10 T) to the azimuthal magnetic field (~1000 T) at the time of observation. We show that the angle of the helical instability structures depends on the available axial magnetic flux in the region that surrounds the target rather than simply the applied magnetic field strength, which indicates compression of magnetic flux leads to the observed helical structures. Magneto-hydrodynamics simulations that include an axially magnetized low-density plasma surrounding the target can reproduce experimentally observed trends in the helical angle with magnetic flux. Understanding the origins of these helical structures enables control over their formation, which allows optimization of implosion stability.