Spintronic devices have received lots of attention recently due to their potential to provide a solution for the presentday challenge of increased power dissipation. Among spintronic devices, domain-wall synaptic devices are speed and energy efficient for solving image classification, speech recognition, and other problems. In this paper, a fully connected neural network (FCNN) is implemented using energy-efficient domain wall-based synaptic devices and transistor-based feedback circuits. The designed FCNN is trained on-chip for the classification of Fisher's Iris dataset. The proposed neural network achieves an accuracy of 95%. The proposed FCNN is 96% and 83.3% efficient in terms of energy and latency respectively when compared to previously proposed hardware for on-chip learning.