Context. The flat-spectrum radio quasar 4C +71.07 is a high-redshift (z = 2.172), gamma-loud blazar whose optical emission is dominated by thermal radiation from the accretion disc. Aims. 4C +71.07 has been detected in outburst twice by the AGILE gamma-ray satellite during the period from the end of October to mid-November 2015, when it reached a gamma-ray flux of the order of F(E > 100 MeV) = (1.2 +/- 0.3) x 10(-6) photons cm (2) s(-1) and F(E > 100 MeV) = (3.1 +/- 0.6) x 10(-6) photons cm(-2) s(-1), respectively, allowing us to investigate the properties of the jet and the emission region. Methods. We investigated its spectral energy distribution by means of almost-simultaneous observations covering the cm, mm, near-infrared, optical, ultraviolet, X-ray, and gamma-ray energy bands obtained by the GASP-WEBT Consortium and the Swift, AGILE, and Fermi satellites. Results. The spectral energy distribution of the second gamma-ray flare (whose energy coverage is more dense) can be modelled by means of a one-zone leptonic model, yielding a total jet power of about 4 x 10(47) erg s(-1). Conclusions. During the most prominent gamma-ray flaring period our model is consistent with a dissipation region within the broad-line region. Moreover, this class of high-redshift, flat-spectrum radio quasars with high-mass black holes might be good targets for future gamma-ray satellites such as e-ASTROGAM.