Knowledge Graph Completion (KGC) involves predicting missing entities or relations. In few-shot KGC, reasoning over unseen relations from only a handful of examples is like solving a mystery with just a few scattered clues. While existing methods have made progress using translational, bilinear, deep learning and few-shot learning approaches, challenges in few-shot relational reasoning remain. Current few-shot learning approaches like Connection Subgraph Reasoner (CSR) cast the problem in subgraph-based edge-mask learning framework, where the model solely relies on the graph representations of the retrieved subgraphs assuming largest common subgraph shared across all support subgraphs. However, these approaches lead to unrelated spurious information that can adversely impact performance of prediction of the missing entity. We introduce FLARE (Few-shot Learning with Attention-guided Relational Subgraph Reasoner), a novel framework that improves KGC by leveraging MLP-based edge attention mechanism for edge scoring, refined node aggregation with attention-weighted edge embeddings and adaptive support graph pooling. The model was evaluated on NELL, FB15K-237 and ConceptNet datasets. Experimental results demonstrate that FLARE consistently outperforms existing baselines across all metrics, thus achieving new state-of-the-art performance.