Multi fidelity Bayesian optimization (MFBO) leverages experimental and or computational data of varying quality and resource cost to optimize towards desired maxima cost effectively. This approach is particularly attractive for chemical discovery due to MFBO's ability to integrate diverse data sources. Here, we investigate the application of MFBO to accelerate the identification of promising molecules or materials. We specifically analyze the conditions under which lower fidelity data can enhance performance compared to single-fidelity problem formulations. We address two key challenges, selecting the optimal acquisition function, understanding the impact of cost, and data fidelity correlation. We then discuss how to assess the effectiveness of MFBO for chemical discovery.