Blazars are among the most energetic objects in the Universe. In 2008 August, Fermi/LAT detected the blazar PKS 1502+106, which showed a rapid and strong gamma-ray outburst followed by high and variable flux over the next months. This activity at high energies triggered an intensive multi-wavelength campaign that also covered the radio, optical, UV, and X-ray bands, indicating that the flare was accompanied by a simultaneous outburst at optical/UV/X-rays and a delayed outburst at radio bands. We explore the phenomenology and physical conditions within the ultra-relativistic jet of the gamma-ray blazar PKS 1502+106. Additionally, we address the question of the spatial localization of the MeV/GeV-emitting region of the source. We used ultra-high angular resolution mm-VLBI observations at 43 and 86GHz complemented by VLBI observations at 15GHz. We also employed single-dish radio data from the F-GAMMA program at frequencies matching the VLBI monitoring. PKS 1502+106 shows a compact core-jet morphology and fast superluminal motion with apparent speeds in the range 5-22c. Estimating Doppler factors along the jet yields values of between ~7 up to ~50. This Doppler factor gradient implies an accelerating jet. The viewing angle towards the source differs between the inner and outer jet, with the former at {theta}~3{deg} and the latter at {theta}~1{deg}, after the jet bends towards the observer beyond 1mas. The de-projected opening angle of the ultra-fast magnetically dominated jet is found to be (3.8+/-0.5){deg}. A single jet component can be associated with the pronounced flare both at high energies and in radio bands. Finally, the gamma-ray emission region is localized at <=5.9pc away from the jet base.