Ribonucleic acids (RNAs) are essential biomolecules involved in gene regulation and molecular recognition. Designing RNA molecules that can bind specific protein targets is crucial for therapeutic applications but remains challenging due to the structural flexibility of RNA and the laborious nature of experimental techniques. We propose RNA-EFM, a novel Energy-based Flow Matching framework for protein conditioned RNA sequence and structure co-design. RNA-EFM integrates biophysical constraints, including the Lennard-Jones potential and sequence-derived free energy, to generate low-energy and biologically plausible RNA conformations. By incorporating an idempotent refinement strategy for iterative structural correction, RNA-EFM consistently outperforms existing baselines, achieving lower RMSD, higher lDDT, and superior sequence recovery across multiple evaluation splits.