Modeling the oxidation of soot particles in flames is a challenging topic both from a chemical point of view and regarding the statistical treatment of the evolution of the soot number density function (NDF). The method of moments is widely-used for the statistical modeling of aerosol dynamics in various applications, and a number of different moment methods have been established and successfully applied to the modeling of soot formation and growth. However, a shortcoming of existing moment methods is the lack of an accurate, numerically robust, and computationally efficient way to treat soot oxidation, especially regarding the prediction of the particle number density. In this work, the recently developed Extended Quadrature Method of Moments (EQMOM) is integrated with a physico-chemical soot model and combined with a treatment for particle removal by oxidation. This leads to a modeling framework for the simulation of coupled inception, growth, coagulation, and oxidation of soot in flames. In EQMOM, the moment equations are closed by reconstructing the soot NDF with a superposition of continuous kernel functions. Various standard distribution functions can be used as kernel functions, and the algorithm has been implemented here using gamma and lognormal distributions. It is shown that and discussed why gamma distributions are more suitable as kernel functions than lognormal distributions in order to accurately predict soot oxidation. The integrated model is validated by comparisons with analytical solutions for the NDF, results from Monte Carlo simulations of soot formation and oxidation in flames, and experimental data.