Federated Learning (FL) is increasingly being adopted in military collaborations to develop Large Language Models (LLMs) while preserving data sovereignty. However, prompt injection attacks-malicious manipulations of input prompts-pose new threats that may undermine operational security, disrupt decision-making, and erode trust among allies. This perspective paper highlights four vulnerabilities in federated military LLMs: secret data leakage, free-rider exploitation, system disruption, and misinformation spread. To address these risks, we propose a human-AI collaborative framework with both technical and policy countermeasures. On the technical side, our framework uses red/blue team wargaming and quality assurance to detect and mitigate adversarial behaviors of shared LLM weights. On the policy side, it promotes joint AI-human policy development and verification of security protocols.