Too many causes to provide an "answer". On the K's the pump is wired off the level sensor.
I'd lift the pump out, disconnect both + & - wires (put hose over ends=no sparks) and directly put wires on the pump, - to ground & hold the + to the battery just as you start the engine.
This will parse a mechanical vs electrical problem.
If it runs ok, it's electrical: get the Clymer manual (M500) to trace power wiring.
If it still sputters & dies, I'd put pressure gauge inline of pump to injector rail. It should be ~38psi.
The regulator may be bad (pinch the hose of rail to regulator to see), but more likely the pump can't keep up.
I've build 3 K bikes from wrecks and worked on many others.