Flavour issues in warped custodial models: $B$ anomalies and rare $K$ decays

We explore the flavour structure of custodial Randall-Sundrum (RS) models in the context of the recently observed deviations in the decay of the $B$ mesons. The anomalies in the $b\rightarrow s ll$ processes can be easily fit with partially composite second generation leptons and third generation quarks. We establish correlation with the parameter space consistent with the flavour anomalies in the neutral current sector and obtain predictions for rare $K$- decay which are likely to be another candle for NP with increased precision. Two scenarios are considered: A) Right handed muon coupled more to NP that the corresponding muon doublets (unorthodox case). Non-universality exists in the right handed sector. B) Standard scenario with anomalies explained primarily by non-universal couplings to the lepton doublets. The prediction for rare $K$-decays are different according to the scenario, thereby serving as a useful discriminatory tool. We note that, in this setup $R(D^*)$ is at best consistent with the SM and increasing the compositeness of the $\tau_L$ generates a net contribution becoming below the SM expectation. This makes this framework fairly predictive and easily verifiable. Finally, we also comment on the implications of flavour violation in the lepton sector and present an explicit example with the implementation of bulk leptonic MFV which helps in alleviating the constraints.