Joint work with Jean-François Martin. The Szemerédi-Trotter theorem bounds the number of incidences between finite sets of points and straight lines in the real plane, and generalisations to other algebraic binary relations play an important role in understanding the interaction between (pseudo)finite sets and field structure in characteristic zero. In positive characteristic, these incidence bounds fail drastically without further restrictions, but may be expected to hold under certain conditions. We confirm this in the case of fields admitting a valuation with finite residue field, e.g. finitely generated extensions of F_p, by seeing that the restricted distality provided by the valuation suffices to trigger a result of Chernikov-Galvin-Starchenko.