Generally there is one on-demand water heater for all fixtures. So if it works for one it should work for all.
There may be a long pipe from the heater to the kitchen. If so it could take a while for hot water to reach the kitchen sink.
On demand systems usually require a high flow for long period to turn "ON". Maybe the kitchen sink flow is not high enough. Or, maybe you turn it "ON" and "OFF" too frequently to get the heater working.
It must sill be under warranty. Take it back to the dealer. Maybe the technician can watch how you use it and give you pointers. The "ON/OFF" trigger may be adjustable.
Sometimes people install a 120 volt heater under the sink for kitchen hot water. That would work when using shore power.