Can TankMate measure flow rates?

No, the TankMate sensor will only be able to tell you the net result of water in vs water out as it takes point in time measurements, it is not a flowmeter or similar that measures in both directions.

So if you're using water and filling the tank at the same time, the unit will not be able to determine either individually, it will only be able to tell you if you had a net water loss or gain over that period of time.

If you're wanting to use it to gauge water usage when you've potentially got water coming and going out at the same time, then you need a flow meter of some sort.

But if you have a way of scheduling the usage vs filling up so that they don't happen at the same time, then the TankMate will work well for you as it will be able to tell you the drop or rise independently.