Connecting flowmeter via USB to a computer
What you've bought is a USB to serial converter. The RX pin 'expects' to see serial data from a UART coming in.

You may be able to fool it into thinking the leading edge of your pulse from your flowmeter is a 'start' bit, so trying to get it to register that it's received a byte (obviously a garbage byte) for each pulse. You will need to run at a low enough baud rate so the pulse has dropped before the end of the byte, so that it can see a valid stop bit, either that or shorten the pulse with a monostable to achieve the same end. How long are the pulses?

You may be better off buying an MCU like an Arduino. They will talk serial to the PC over their USB, and are programmable to do just about anything you are likely to want with the pins. It may seem like a sledgehammer to crack a nut, but what a useful sledgehammer once you've learned how to use it, much more useful and no more expensive than a USB to parallel converter.