Keyboard typing with finger movements is a versatile digital interface for users with diverse skills, needs, and preferences. Currently, such an interface does not exist for people with paralysis. We developed an intracortical brain-computer interface (BCI) for typing with attempted flexion/extension movements of three finger groups on the right hand, or both hands, and demonstrated its flexibility in two dominant typing paradigms. The first paradigm is "point-and-click" typing, where a BCI user selects one key at a time using continuous real-time control, allowing selection of arbitrary sequences of symbols. During cued character selection with this paradigm, a human research participant with paralysis achieved 30-40 selections per minute with nearly 90% accuracy. The second paradigm is "keystroke" typing, where the BCI user selects each character by a discrete movement without real-time feedback, often giving a faster speed for natural language sentences. With 90 cued characters per minute, decoding attempted finger movements and correcting errors using a language model resulted in more than 90% accuracy. Notably, both paradigms matched the state-of-the-art for BCI performance and enabled further flexibility by the simultaneous selection of multiple characters as well as efficient decoder estimation across paradigms. Overall, the high-performance interface is a step towards the wider accessibility of BCI technology by addressing unmet user needs for flexibility.