What's the flow rate like at the kitchen, and is it a mixer valve (likely)? Did it ever work properly at the kitchen sink?
There is a min-flow requirement to get the tankless to light-off- cracking it open at a dribble won't cut it, even if once it lights it can be taken down to a fairly low flow without flaming out. Min-flow on the N069-M is 0.5 gpm- below that it can't light, or will turn off. If the mixer at the kitchen is defective and only delivering cold or not enough flow on the hot side, that could cause the symptom.
Turn off the shutoff valve to cold side of the mixer, see if that affects the total flow when the mixer handle swung all the way to "hot", &/or the ignition issue.