We consider a probe codimension-2 brane inflation scenario in a warped six-dimensional flux compactification. Our background model is Salam-Sezgin gauged supergravity with codimension-2 brane sources, which preserve N=1 supersymmetry. The model has a modulus, which is stabilized by means of a cap regularization of the codimension-2 singularities, with appropriate dilaton potentials on the ring interface of the caps with the bulk. We discuss the cosmological evolution of the worldvolume of a probe codimension-2 brane when it moves along the radial direction of the internal space. In order to have slow-roll inflation, one needs the warping of the internal space to be weak, in contrast to the recent string inflation constructions with strong warping. We discuss the parameter range that the inflation is in agreement with the observationally inferred parameters and which furthermore is consistent with the probe-brane approximation. We provide arguments pointing that the probe-brane approximation is a good assumption if the probe-brane is not exactly conical and show with a multibrane solution that the mild warping needed for a slow-roll inflation is not spoiled by the probe brane.