This paper proposes the concepts of ESG information flows and a predictable framework of ESG flows based on AR process, and studies how ESG information flows are incorporated into and affect a dynamic portfolio with transaction costs. Two methods, called the ESG factor model and the ESG preference model, are considered to embed ESG information flows into a dynamic mean-variance model. The dynamic optimal portfolio can be expressed as a traditional optimal portfolio without ESG information and a dynamic ESG preference portfolio, and the impact of ESG information on optimal trading is explicitly analyzed. The rich numerical results show that ESG information can improve the out-of-sample performance, and ESG preference portfolio has the best out-of-sample performance including the net returns, Sharpe ratio and cumulative return of portfolios, and contribute to reducing risk and transaction costs. Our dynamic trading strategy provides valuable insights for sustainable investment both in theory and practice.