Can I use a "universal" flush valve (or different brand) in my Kohler toilet?
It depends on the configuration of the flush valve. If it's the type with a 3-4 inch plastic tube that when lifted allows water to flush than you need to use that specific valve type from Kohler. If not and the valve is mounted through a standard (3/4 inch +/-) opening to the supply line you should be able to swap in any valve with minor adjustments to the lift handle and flapper. Post a photo of the Kohler valve.