Understanding the mechanisms of plasticity in structural steels is essential for the operation of next-generation fusion reactors. Elemental composition, particularly the amount of Cr present, and irradiation can have separate and synergistic effects on the mechanical properties of ferritic/martensitic steels. The study of ion-irradiated FeCr alloys is useful for gaining a mechanistic understanding of irradiation damage in steels. Previous studies of ion-irradiated FeCr did not clearly distinguish between the nucleation of dislocations to initiate plasticity, and their propagation through the material as plasticity progresses. In this study, Fe3Cr, Fe5Cr, and Fe10Cr were irradiated with 20 MeV Fe$^{3+}$ ions at room temperature to nominal doses of 0.01 dpa and 0.1 dpa. Nanoindentation was carried out with Berkovich and spherical indenter tips to study the nucleation of dislocations and their subsequent propagation. The presence of irradiation-induced defects reduced the theoretical shear stress and barrier for dislocation nucleation. The presence of Cr further enhanced this effect due to increased retention of irradiation defects. However, this combined effect is still small compared to dislocation nucleation from pre-existing sources such as Frank-Read sources and grain boundaries. The yield strength, an indicator of dislocation mobility, of FeCr increased with irradiation damage and Cr. The increased retention of irradiation defects due to the presence of Cr also further increased the yield strength. Reduced work hardening capacity was also observed following irradiation. The synergistic effects of Cr and irradiation damage in FeCr appear to be more important for the propagation of dislocations, rather than their nucleation.