  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 stabilised by means of a cap
regularisation 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 world-volume 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.
