Ligand-induced protein allostery plays a central role in modulating cellular signalling pathways. Here using the conserved cyclic nucleotide-binding domain of protein kinase A's (PKA) regulatory subunit as a prototype signalling unit, we combine long-timescale, all-atom molecular dynamics simulations with Markov state models to elucidate the conformational ensembles of PKA's cyclic nucleotide-binding domain A for the cAMP-free (apo) and cAMP-bound states. We find that both systems exhibit shallow free-energy landscapes that link functional states through multiple transition pathways. This observation suggests conformational selection as the general mechanism of allostery in this canonical signalling domain. Further, we expose the propagation of the allosteric signal through key structural motifs in the cyclic nucleotide-binding domain and explore the role of kinetics in its function. Our approach integrates disparate lines of experimental data into one cohesive framework to understand structure, dynamics and function in complex biological systems.