Oscillatory shear flow of poly[B-(methylamino)borazine] was studied for suitability as a meltspinnable material. Shear rheology experiments show that viscosity of molten poly[B-(methylamino)borazine] is temperature dependent following an Arrhenius-type equation. The high value of the flow activation energy is caused by the presence of branched chains and cross-linked portions in the polymer network which supply an intrinsic rigidity to the molecular architecture. Dynamic rheological properties of polymers were measured at their spinning temperatures as a function of the oscillatory frequency. The frequency dependence of the storage and loss moduli as well as the damping factor shows that an appropriate ratio of viscosity to elasticity, i.e., 1 < tan δ < 2.3, is necessary to allow for extrusion while a specific range of elasticity, i.e., 104 < G′ [Pa] < 3 × 104, is required for drawing the emerging molten fibers as they solidify into fine-diameter solid filaments without loss of cohesion.