Plumbing Questions? Ask a Plumbing Expert.
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What do you have for a water heater? does it have a re-circulating pump?
It sounds like the flow from the kitchen faucet is not adequate to turn the water heater on. Try this, turn on just the hot water in just the kitchen sink and tell me if the Rinnai fires up
Did you try running the kitchen hot water? did the Rinnai fire up?