Flavor observables are usually computed with the help of the electroweak Hamiltonian which separates the perturbative from the non-perturbative regime. The Wilson coefficients are calculated perturbatively, while matrix elements of the operators require non-perturbative treatment, e.g. through lattice simulations. The resulting necessity to compute the transformation between the different renormalization schemes constitutes an important source of uncertainties. I will discuss how the gradient flow formalism potentially provides an elegant solution to this problem.