We theoretically demonstrate the generation of Kerr microcombs in integrated graphene-clad silicon-nitride slot waveguide ring resonators. In our work, the graphene monolayer provides the enabling nonlinearity, by means of its third-order surface conductivity. We use the Lugiato-Lefever equation framework, modified to incorporate the frequency dispersion of all eigenmode properties, including nonlinearity, in an ultrawide octave-spanning spectrum. The waveguide parameters are rigorously computed by a full-vector mode solver where we input graphene's full set of electromagnetic properties, both linear and nonlinear; the latter are extracted by quantum perturbation formulas, as a function of graphene's chemical potential and equilibrium lattice temperature. Our results show the potential of graphene, as a 2D material with electrically tunable linear and nonlinear response, for Kerr combs or other integrated nonlinear devices, such as mode-locked and Q-switched lasers.