In this paper we study the boundary effects for off-critical integrable field theories which have close analogues with integrable lattice models. Our models are the SU (2) k ⊗ SU (2) l/SU (2) k+l coset conformal field theories perturbed by an integrable boundary and bulk operators. The boundary interactions are encoded into the boundary reflection matrix. Using the thermodynamic Bethe ansatz (TBA) method, we verify the flows of the conformal BCs by computing the boundary entropies. These flows of the BCs have direct interpretations for the fusion restricted solid-on-solid (RSOS) lattice models. For super conformal field theories (CFTs) (k = 2) we show that these flows are possible only for the Neveu-Schwarz sector and are consistent with the lattice results. The models we consider cover a wide class of integrable models. In particular, we show how the impurity spin is screened by electrons for the k-channel Kondo model by taking the l → ∞ limit. We also study the problem using an independent method based on the boundary roaming TBA. Our numerical results are consistent with the boundary CFTs and RSOS TBA analysis.