FlowEvo is a training-free framework designed to enable large language model (LLM) agents to achieve self-evolution through the simultaneous co-evolution of workflows and executable skills during inference. Unlike traditional methods that discard discovered procedures or rely on offline skill libraries, FlowEvo compiles successful task workflows into callable, reusable skills stored in a persistent bank. These retrieved skills are utilized either via direct execution or as contextual guidance for synthesizing new workflows. To maintain efficiency and prevent performance degradation, the framework monitors the downstream utility of each skill and suppresses those that trigger negative transfer. Utilizing a shared GPT-4o-mini backbone, FlowEvo demonstrated superior performance across several benchmarks, including ALFWorld, HumanEval, MBPP, GSM8K, and MATH-500. Notably, on the ALFWorld benchmark, the framework achieved an 85.6% accuracy rate, representing a 26.4-point improvement over the strongest baseline while consuming approximately one-third of the tokens. Furthermore, extensive testing across ten base models ranging from 7B to 671B parameters showed that FlowEvo outperformed the ExpeL baseline in 49 out of 50 model-dataset comparisons, proving its robustness and scalability across varying model sizes.