The health management of batteries is a key enabler for the adoption of Electric Vertical Take-off and Landing vehicles (eVTOLs). Currently, few studies consider the health management of eVTOL batteries. One distinct characteristic of batteries for eVTOLs is that the discharge rates are significantly larger during take-off and landing, compared with the battery discharge rates needed for automotives. Such discharge protocols are expected to impact the long-run health of batteries. This paper proposes a data-driven machine learning framework to estimate the state-of-health and remaining-useful-lifetime of eVTOL batteries under varying flight conditions and taking into account the entire flight profile of the eVTOLs. Three main features are considered for the assessment of the health of the batteries: charge, discharge and temperature. The importance of these features is also quantified. Considering battery charging before flight, a selection of missions for state-of-health and remaining-useful-lifetime prediction is performed. The results show that indeed, discharge-related features have the highest importance when predicting battery state-of-health and remaining-useful-lifetime. Using several machine learning algorithms, it is shown that the battery state-of-health and remaining-useful-life are well estimated using Random Forest regression and Extreme Gradient Boosting, respectively.