We calculate the angular power spectrum of the cosmic microwave background temperature fluctuations induced by the kinetic Sunyaev-Zel'dovich (kSZ) effect from the epoch of reionization (EOR). We use detailed N-body+radiative-transfer simulations to follow inhomogeneous reionization of the intergalactic medium. For the first time, we take into account the self-regulation of reionization: star formation in low-mass dwarf galaxies (10(8) M-circle dot less than or similar to M less than or similar to 10(9) M-circle dot) or minihalos (10(5) M-circle dot less than or similar to M less than or similar to 10(8) M-circle dot) is suppressed if these halos form in the regions that were already ionized or Lyman-Werner dissociated. Some previous work suggested that the amplitude of the kSZ power spectrum from the EOR can be described by a two-parameter family: the epoch of half-ionization and the duration of reionization. However, we argue that this picture applies only to simple forms of the reionization history which are roughly symmetric about the half-ionization epoch. In self-regulated reionization, the universe begins to be ionized early, maintains a low level of ionization for an extended period, and then finishes reionization as soon as high-mass atomically cooling halos dominate. While inclusion of self-regulation affects the amplitude of the kSZ power spectrum only modestly (similar to 10%), it can change the duration of reionization by a factor of more than two. We conclude that the simple two-parameter family does not capture the effect of a physical, yet complex, reionization history caused by self-regulation. When added to the post-reionization kSZ contribution, our prediction for the total kSZ power spectrum is below the current upper bound from the South Pole Telescope. Therefore, the current upper bound on the kSZ effect from the EOR is consistent with our understanding of the physics of reionization.