We show that for every non-elementary hyperbolic group, an associated topological flow space admits a coding based on a transitive subshift of finite type. Applications include regularity results for Manhattan curves, the uniqueness of measures of maximal Hausdorff dimension with potentials, and the real analyticity of intersection numbers for families of dominated (Anosov) representation, thus providing direct proof of a result established by Bridgeman et al. in 2015. Joint work with Steve Cantrell (Chicago).