The effect of magnetic field on the flow-phase diagram of discotic nematic liquid crystalline polymers (LCPs) is analyzed with the extended Doi theory in which the molecular shape parameter is defined at negative one. The evolution equation for the probability function of the LCP molecules is solved without any closure approximations. The transition among flow-orientation modes, such as tumbling, wagging and aligning defined similar to the rodlike LCPs, are strongly affected by the magnetic fields parallel to the flow direction.