Time series Forecasting with large language models (LLMs) requires bridging numerical patterns and natural language. Effective forecasting on LLM often relies on extensive pre-processing and fine-tuning. Recent studies show that a frozen LLM can rival specialized forecasters when supplied with a carefully engineered natural-language prompt, but crafting such a prompt for each task is itself onerous and ad-hoc. We introduce FLAIRR-TS, a test-time prompt optimization framework that utilizes an agentic system: a Forecaster-agent generates forecasts using an initial prompt, which is then refined by a refiner agent, informed by past outputs and retrieved analogs. This adaptive prompting generalizes across domains using creative prompt templates and generates high-quality forecasts without intermediate code generation. Experiments on benchmark datasets show FLAIRR-TS improves forecasting over static prompting and retrieval-augmented baselines, approaching the performance of specialized prompts.FLAIRR-TS provides a practical alternative to fine-tuning, achieving strong performance via its agentic approach to adaptive prompt refinement and retrieval.