In air traffic control (ATC), Key Information Recognition (KIR) of ATC instructions plays a pivotal role in automation. The field's specialized nature has led to a scarcity of related research and a gap with the industry's cutting-edge developments. Addressing this, an innovative end-to-end deep learning framework, Small Sample Learning for Key Information Recognition (SLKIR), is introduced for enhancing KIR in ATC instructions. SLKIR incorporates a novel Multi-Head Local Lexical Association Attention (MHLA) mechanism, specifically designed to enhance accuracy in identifying boundary words of key information by capturing their latent representations. Furthermore, the framework includes a task focused on prompt, aiming to bolster the semantic comprehension of ATC instructions within the core network. To overcome the challenges posed by category imbalance in boundary word and prompt discrimination tasks, tailored loss function optimization strategies are implemented, effectively expediting the learning process and boosting recognition accuracy. The framework's efficacy and adaptability are demonstrated through experiments on two distinct ATC instruction datasets. Notably, SLKIR outperforms the leading baseline model, W2NER, achieving a 3.65% increase in F1 score on the commercial flight dataset and a 12.8% increase on the training flight dataset. This study is the first of its kind to apply small-sample learning in KIR for ATC and the source code of SLKIR will be available at: https://github.com/PANPANKK/ATC_KIR.