Employing results from a recent determination of the scalar Kpi form factor F-0(Kpi) within a coupled channel dispersion relation analysis [1], in this work we calculate the slope and curvature of F-0(Kpi)(t) at zero momentum transfer. Knowledge of the slope and curvature of the scalar Kpi form factor, together with a recently calculated expression for F-0(Kpi)(t) in chiral perturbation theory at order p(6), enable to estimate the O(p(6)) chiral constants C-12(r) (M-rho) = (0.3 +/- 5.4) . 10(-7) and (C-12(r) + C-34(r)) (M-rho) = (3.2 +/- 1.5) . 10(-6). Our findings also allow to estimate the contribution coming from the C-i to the vector form factor F-+(Kpi)(0) which is a crucial ingredient for a precise determination of \V-us\ from K-l3 decays. Our result F-+(Kpi)(0)\C-i(r) = -0.018 +/- 0.009, though inflicted with large uncertainties, is in perfect agreement with a previous estimate by Leutwyler and Roos already made twenty years ago.