We present a complete calculation of the photon +1 jet rate in e(^+)e(^-) annihilation up to O(aa(_s)). Although formally of next-to-leading order in perturbation theory, this calculation contains several ingredients appropriate to a next-to-next-to-leading order calculation of jet observables. No such calculation has been performed before, and the work discussed here represents a first step in that direction. In particular, we describe a generalization of the commonly used phase space slicing method to isolate the singularities present when more than one particle is unresolved. More precisely, we provide an analytic evaluation of the following multiple unresolved factors: triple collinear factor, soft/collinear factor and double single collinear factor. By comparing the results of our calculation with the existing data on the photon +1 jet rate from the ALEPH Collaboration at CERN, we make a new determination of the process-independent non-perturbative quark-to-photon fragmentation function D(_q-γ)(z,μ(_F)) at O(aa(_s)). at As a first application of this measurement allied with our improved perturbative calculation, we determine the dependence of the isolated photon -fl jet cross section in a democratic clustering approach on the jet resolution parameter y(_cut) at next-to-leading order. Inclusion of the next-to-leading order corrections to this observable considerably improves the agreement between theoretical prediction and experimental data.