Exchangeable liquid crystal elastomers (XLCEs), an emerging class of recyclable polymer materials, consist of liquid crystalline polymers which are dynamically crosslinked. We develop a macroscopic continuum model by incorporating the microscopic dynamic features of the cross-links, which can be utilized to understand the viscoelasticity of the materials together with the dynamic nematic order. As applications of the model, we study the rheological responses of XLCEs in three cases: stress relaxation, strain ramp, and creep compliance, where the materials show interesting rheology as an interplay between the dynamic nematic order of the mesogenic units, the elasticity from the network structure, and the dissipation due to chain exchange reactions. Not only being useful in understanding the physical mechanism underlying the fascinating characteristics of XLCEs, this work can also guide their future fabrications with desired rheological properties.