We present an inverse weak value amplification (IWVA) scheme to perform precision frequency measurements in an integrated optics environment. The IWVA technique allows us to amplify small signals by introducing a weak perturbation to the system and performing a post-selection on the data. A Bragg grating with two band gaps is used to convert the optical frequency into a phase, and a perturbation is applied to the mode coefficients. We demonstrate the advantages of a Bragg grating with two band gaps for obtaining high transmission and low group velocity. We numerically model the interferometer, and demonstrate that we obtain the desired amplification effect. By using an on-chip device instead of a free space implementation, precision measurements can be carried out in a small volume with reliable performance.