In this work we consider a DBI Galileon (DBIG) inflationary model and constrain its parameter space with the Planck 2015 and BICEP2/Keck array and Planck (BKP) joint analysis data by means of a potential independent analysis. We focus our attention on inflationary solutions characterized by a constant or varying sound speed as well as warp factor. We impose bounds on stringy aspects of the model, such as the warp factor $\left(f\right)$ and the induced gravity parameter $\left(\tilde{m}\right)$. We study the parameter space of the model and find that the tensor-to-scalar ratio can be as low as $r\simeq6\times10^{-4}$ and inflation happens to be at GUT scale. In addition, we obtain the tilt of the tensor power spectrum and test the standard inflationary consistency relation $\left(r=-8n_{t}\right)$ against the latest bounds from the combined results of BKP+Laser Interferometer Gravitational-Waves Observatory (LIGO), and find that DBIG inflation predicts a red spectral index for the tensor power spectrum.