We theoretically study the spin dependent transport through a magnetic double tunnel junction system, which consists of a nonmagnetic metal island sandwiched by two ferromagnetic electrodes. The transport model in both cotunneling and sequential tunneling regimes is based on the master equation, and systematically incorporates the effects of both intraisland spin-flip (SF) and SF during tunneling between the electrode and the island. We found that the tunnel magnetoresistance (TMR) in the cotunneling regime is impervious to either the intraisland SF or the tunneling SF effect. On the other hand, in the sequential tunneling regime, the TMR decreases with the increasing intraisland SF rate Γ and tunneling SF probability η (η<0.5). However, when the tunneling SF is much stronger, i.e., η>0.5, the TMR is enhanced by increasing the tunneling SF probability. The increase in the temperature suppresses the cotunneling TMR, whereas the sequential tunneling TMR is found to be more robust to temperature variation.