The collisional magnetic reorientation rate constant g R is measured for magnetically trapped atomic dysprosium (Dy), an atom with large magnetic dipole moments. Using buffer gas cooling with cold helium, large numbers (>10 11 ) of Dy are loaded into a magnetic trap and the buffer gas is subsequently removed. The decay of the trapped sample is governed by collisional reorientation of the atomic magnetic moments. We find g R = 1.9 ± 0.5 × 10 −11 cm 3 s −1 at 390 mK. We also measure the magnetic reorientation rate constant of holmium (Ho), another highly magnetic atom, and find g R = 5 ± 2 × 10 −12 cm 3 s −1 at 690 mK. The Zeeman relaxation rates of these atoms are greater than expected for the magnetic dipole-dipole interaction, suggesting that another mechanism, such as an anisotropic electrostatic interaction, is responsible. Comparison with estimated elastic collision rates suggests that Dy is a poor candidate for evaporative cooling in a magnetic trap.