In this paper, we study the properties of accretion flow including its spectral features in Johannsen and Psaltis (JP) non-Kerr spacetime. In doing so, we numerically solve the governing equations that describe the flow motion around the compact objects in a general relativistic framework, where spin (ak ) and deformation parameters (ε) demonstrate the nature of the central source, namely black hole (BH) or naked singularity (NS). With this, we obtain all possible classes of global accretion solutions (i.e., O, A, W and I-type) by varying the energy (E) and angular momentum (λ) of the relativistic accretion flow, and examine the role of thermal bremsstrahlung emission in studying the spectral energy distributions (SEDs) of the accretion disc. We divide the parameter space in λ-E plane in terms of the different classes of accretion solutions for BH and NS models. We further calculate the disc luminosity (L) corresponding to these accretion solutions, and observe that I-type solutions yield higher L and SEDs than the remaining types of solutions for both BH and NS models. For BH model, SEDs for W and I-type solutions differ significantly from the results for O and A-type solutions for low E values. On the contrary, for NS model, SEDs for different accretion solutions are identical in the whole parameter space of λ and E. We also examine the effect of ε on the SEDs and observe that a non-Kerr BH yields higher SEDs than the usual Kerr BH. Finally, for accretion solutions of identical E and λ, we compare the SEDs obtained from BH and NS models, and find that naked singularity objects produce more luminous power spectra than the black holes.