The increasing availability of condition monitoring data for aircraft components has incentivized the development of Remaining Useful Life (RUL) prognostics in the past years. However, only few studies consider the integration of such prognostics into maintenance planning. In this paper we propose a dynamic, predictive maintenance scheduling framework for a fleet of aircraft taking into account imperfect RUL prognostics. These prognostics are periodically updated. Based on the evolution of the prognostics over time, alarms are triggered. The scheduling of maintenance tasks is initiated only after these alarms are triggered. Alarms ensure that maintenance tasks are not rescheduled multiple times. A maintenance task is scheduled using a safety factor, to account for potential errors in the RUL prognostics and thus avoid component failures. We illustrate our approach for a fleet of 20 aircraft, each equipped with 2 turbofan engines. A Convolution Neural Network is proposed to obtain RUL prognostics. An integer linear program is used to schedule aircraft for maintenance. With our alarm-based maintenance framework, the costs with engine failures account for only 7.4% of the total maintenance costs. In general, we provide a roadmap to integrate imperfect RUL prognostics into the maintenance planning of a fleet of vehicles.