Quantum Chromodynamics, the study of quarks, gluons and their interaction, is a field yet to be fully understood. The strength of the coupling makes perturbative predictions less reliable than those of weakly coupled Quantum Electrodynamics. Therefore, based on the path integral formalism, lattice calculations were introduced and proven to be a powerful tool. However, the numerical results come with systematic deviations from the physical world that make it hard to extrapolate to the continuum limit. These can be reduced by choosing the lattice action and observable cleverly. Furthermore, lattice results are often very noisy, again making it hard to extract information. Gradient flow has proven to be a useful tool to resolve this problem. Its lattice formulation again suffers from systematic deviations that can be reduced via a more elaborate definition, the Zeuthen flow. In lattice studies, this improved gradient flow is used to measure color-electric as well as color-magnetic correlators which are expectation values of components of the QCD gauge field strength tensor. They contain information about propagation of heavy quarks in the quark-gluon plasma. Lattice perturbation theory is used in this work to derive their leading order behaviour which allows for easier extrapolation to the continuum and zero flow. In addition, the action density which can be used to measure the gauge coupling on the lattice is expanded in the lattice spacing for various combinations of action, flow and operator to both simplify continuum extrapolation and to see which combinations are to be preferred.