At what UART baud rate is hardware flow control required?
It is not data rate that matters; we use CTS / RTS (or XON / XOFF for software flow control) where a possibility of a receiver overflow exists, although admittedly that is more likely at higher data rates.

If a receiver cannot empty its buffers quickly enough, then it should deassert CTS (in response to which, the transmitter will assert RTS if there is more data to transmit).

Note that the transmitter may experience a buffer underrun in which case it should deassert RTS (because there is no valid data to send).

So it comes down to how fast the buffers can be moved - that is more likely to be an issue at higher data rates but it is completely implementation dependent; there is no single speed.