The degree of coherence in a hybrid system composed of superconducting flux-qubits and an electron ensemble is analysed. Both, the interactions among the electrons and among the superconducting flux-qubits are taken into account. The time evolution of the hybrid system is solved exactly, and discussed in terms of the reduced density matrix of each subsystem. It is seen that the inclusion of a line width, for the electrons and for the superconducting flux-qubits, influences the pattern of spin-squeezing and the coherence of the superconducting flux qubits.