The molecular details governing transcription factor (TF) binding and the formation of accessible chromatin are not yet quantitatively understood - including how sequence context modulates affinity, how TFs search DNA, the kinetics of TF occupancy, and how motif grammars coordinate binding. To resolve these questions for a human TF, erythroid Kruppel-like factor (eKLF/KLF1), we quantitatively compare, in high throughput, in vitro TF binding rates and affinities with in vivo single molecule TF and nucleosome occupancies across engineered DNA sequences. We find that 40-fold flanking sequence effects on affinity are consistent with distal flanks tuning TF search parameters and captured by a linear energy model. Motif recognition probability, rather than time in the bound state, drives affinity changes, and in vitro and in nuclei measurements exhibit consistent, minutes-long TF residence times. Finally, pairing in vitro biophysical parameters with thermodynamic models accurately predicts in vivo single-molecule chromatin states for unseen motif grammars.