We propose a new model of flavour chiral symmetry breaking in a(2+1)-dimensional defect gauge theory of strongly coupled fermions byintroducing probe D5/anti-D5-flavour branes on the conifold. After working outthe flavour brane embeddings at zero temperature, we thoroughly investigate thespectra of small fluctuations on the world volume of the flavour branes (mesonspectrum) and conclude that they are free of tachyons. Thus the proposed probebrane embedding is stable. Moreover, we introduce finite temperature and anexternal magnetic field and study the thermodynamics of the resultingconfigurations. Namely, we compute the free energies, entropies, heatcapacities and magnetisations. The results are used to establish a detailedphase diagram of the model. We find that the effect of magnetic catalysis ofchiral symmetry breaking is realised in our model and show that themeson-melting phase transition coincides with the chiral symmetry breakingphase transition. Furthermore, we show that the model is in a diamagneticphase.