There is a range of practical problems where advanced engineering heterogeneous materials undergo chemical transformations. The primary example of such system is energy storage materials, in particular anodes of Li-ion batteries containing active Si particles. The exploitation of such anodes involves extreme volumetric expansion of the active particles during the chemical reaction. The expansion is causing mechanical stress, which, in turn, influences the kinetics of chemical reactions even up to their arrest. A particular reaction between Si and Li is localised, as well as a number of other reactions, such as oxidation or precipitate formation. The model presented in this paper accounts for the kinetics of the reactions in a collection of particles inside a matrix material. The microstructure is modelled using the multiscale mean-field (MF) framework based on the incremental Mori-Tanaka (IMT) method. This is the first application of a multiscale MF technique to modelling reaction front kinetics in particles and linking the intra-particle kinetics with the response of the matrix. A number of physical effects arising from the influence of the deformation mechanisms of the matrix on the kinetics of the intra-particle reactions is investigated. Furthermore, the applicability of the proposed model and the IMT homogenisation scheme is studied by comparison to the full-field simulations in the cases of small and finite strains.