We present an analysis of the radial angular profile of the galacto-isotropic (GI) γ -ray flux - the statistically uniform flux in angular annuli centred on the Galactic centre. Two different approaches are used to measure the GI-flux profile in 85 months of Fermi-Large Area Telescope data: the Brock-Dechert-Scheinkman statistical method which identifies spatial correlations, and a new Poisson-ordered-pixel method which identifies non-Poisson contributions. Both methods produce similar GI-flux profiles. The GI-flux profile is well described by an existing model of bremsstrahlung, π0 production, inverse Compton scattering, and the isotropic background. Discrepancies with data in our full-sky model are not present in the GI component, and are therefore due to mismodelling of the non-GI emission. Dark matter annihilation constraints based solely on the observed GI profile are close to the thermal weakly interacting massive particle cross-section below 100 GeV, for fixed models of the dark matter density profile and astrophysical γ -ray foregrounds. Refined measurements of the GI profile are expected to improve these constraints by a factor of a few.