Over the last decade the gradient flow formalism has become an
important tool for lattice simulations of Quantum Chromodynamics. It
offers remarkable renormalization properties which pave the way for
cross-fertilization between perturbative and lattice calculations. In
this contribution we report on the construction of the flowed operator
product expansion for the current-current operators of the electroweak
Hamiltonian at NNLO QCD. This allows for simpler transformations
between lattice and perturbative schemes and might reduce the
uncertainties of theoretical predictions for low-energy flavor
observables.