Controlling hybrid systems is mostly very challenging due to the variety of dynamics these systems can exhibit. Inspired by the concept of differential flatness of nonlinear continuous systems and their inherent invertibility property, the present contribution is focused on explicit input trajectory calculation. To this end, a new class of hybrid systems called Flat Hybrid Automata is introduced as a realisation of deterministic, reachable and explicitly invertible hybrid automata. Relevant system properties are derived, an approach for construction and for trajectory calculation is proposed and two demonstrative examples are presented. The results constitute a generalisation of control of invertible hybrid systems which is very useful if, e.g., fast reaction for stabilisation or transitions is relevant.