Blockchain-based Internet of Things (IoT) applications require flexible, fast, and low-power hashing hardware to ensure IoT data integrity and maintain blockchain network confidentiality. However, existing hashing hardware poses challenges in achieving high performance and low power and limits flexibility to compute multiple hash functions with different message lengths. This paper introduces the flexible and energy-efficient crypto-processor (FECP) to achieve high flexibility, high speed, and low power with high hardware efficiency for blockchain-based IoT applications. To achieve these goals, three new techniques are proposed, namely the crypto arithmetic logic unit (Crypto-ALU), dual buffering extension (DBE), and local data memory (LDM) scheduler. The experiments on ASIC show that the FECP can perform various hash functions with a power consumption of 0.239-0.676W, a throughput of 10.2-3.35Gbps, energy efficiency of 4.44-14.01Gbps/W, and support up to 8916-bit message input. Compared to state-of-art works, the proposed FECP is 1.65-4.49 times, 1.73-21.19 times, and 1.48-17.58 times better in throughput, energy efficiency, and energy-delay product (EDP), respectively.