We address the importance of the dynamic molecular ink concentration at a polymer stamp/substrate interface during microcontact displacement or insertion printing. We demonstrate that by controlling molecular flux, we can influence both the molecular-scale order and the rate of molecular exchange of self-assembled monolayers (SAMs) on gold surfaces. Surface depletion of molecular ink at a polymer stamp/substrate interface is driven predominantly by diffusion into the stamp interior; depletion occurs briefly at the substrate by SAM formation, but diffusion of molecules into the bulk of the stamp dominates over practical experimental time scales. As contact time is increased, the interface concentration varies significantly due to diffusion, affecting the quality and coverage of printed films. Controlling interfacial concentration improves printed film reproducibility and the fractional coverage of multicomponent films can be controlled to within a few percent. We first briefly review the important aspects of molecular ink diffusion at a stamp interface and how it relates to experimental duration. We then describe two examples that illustrate control over ink transfer during experiments: the role of contact time on monolayer reproducibility and molecular order, and the fine control of fractional monolayer coverage for the displacement printing of 1-adamantanethiolate SAMs by 1-dodecanethiol.