Mechanical energy conversion via the direct flexomagnetic effect, the coupling between strain gradients and magnetic induction, is essential for designing next-generation nanostructured sensors. Current literature lacks evaluations of the induced magnetic induction, B_z, outside a bending piezo-flexomagnetic nanobeam (PFNB). Existing models assume magnetic isolation i.e., B_z=0 at the transverse surfaces, confining the magnetic scalar potential ψ within the beam. However, capturing realistic field propagation requires ψ continuity across the beam-air interface. We propose a 1D Timoshenko beam formulation coupled with a 2D magnetostatic domain to ensure field consistency. The discretization utilizes a hybrid mesh of 1D Hermite beam elements and 2D nine-node Lagrange quadrilaterals, ensuring C1 mechanical continuity and accurate resolution of scalar magnetic potential gradients. Derived via the Virtual Work principle, the governing equations are solved using a monolithic, symmetric but indefinite solver. This enables studying magnetic quantities both within and beyond the beam section. Accounting for magnetic quantities in the air domain produces variations from isolated analytical models, though results align within 5% when the air domain is removed to simulate isolation. Sensitivity analysis of this beam reveals that while B_z responds strongly to the values of piezomagnetic coefficient, the magnetic potential difference across the beam responds to flexomagnetic coefficient.