We present a measurement of the mass difference between the two B^0 mass eigenstates, Delta m_d, using a flavor method based on correlations of B meson flavor with the charge of other particles produced in ppbar collisions at sqrt s = 1.8 TeV/c^2. Such correlations are expected to arise from b quark hadronization and from B^** decays. B mesons are partially reconstructed using the semileptonic decays B^0 -> l^+D^(*)- X and B^+ -> l^+D-bar^0 X. We obtain Delta m_d = 0.471^+0.078_ -0.068(stat) +\- 0.034(syst) \hbar ps^-1, and measure the efficiency and purity of this flavor tagging method for both charged and neutral B mesons.