Have you checked the raw water for the same taste? If not you should put the softener in by pass and run water to all sink faucets for a few minutes to flush the lines and then at the kitchen sink, let it run for a few minutes and taste it. Or if you have your own well and can get water from the pressure tank to taste, do that.
If no salty taste then the most common cause of salty water is incomplete rinse, which since the drain line is not blocked or kinked should be eliminated as a potential cause, could mean there is too much salt being used to be successfully rinsed out in the length of time the rinse runs for. So is the water level in the salt tank the same as it used to be before the problem started or higher than normal? Maybe a drain line flow control button is partially blocked. If I'm right that would be inside the control valve on a Kinetico. Probably where the drain line connects to the valve. Let us know what you find.