Heater takes more than 1 minute to get water to kit faucet , then temp fluctuates

1) Guesses: Sounds like a bad single-handled faucet cartridge, or low water flow at faucet, or clogged water filter.
Replace faucet cartridge, clean the aerator, and/or clean sediment out of pipes below sink, and clean water filter at tankless unit each month.

2) For exact measure of problem:
Typical faucet can have 2 gallon per minute flow rate.
2 gpm flow rate means faucet fills 1 gallon container in 30 seconds. Test faucet using 1 gallon container and a cooking timer to get flow rate.
Clean aerator to improve flow rate. Compare kitchen flow rate with other faucets in home.
http://waterheatertimer.org/Low-hot-water-pressure.html

Most homes have 1/2" diameter pipe running to kitchen faucet.
100 feet of 1/2" diameter pipe holds 1.2 gallons of water. This assumes no sediment build-up inside pipes.
http://waterheatertimer.org/Water-heater-recirculation-system.html

Assuming only hot is turned on: If faucet is 100 feet away from water heater, and pipe diameter is unobstructed 1/2" diameter, and faucet has 2 gallon per minute water flow, then hot water should arrive in 36 seconds.
50 feet away, and hot water should arrive in 18 seconds.

If kitchen has single handled faucet, and the handle is raised in the middle, then equal amounts of hot and cold water are drawn at same time. This doubles amount of time for hot water to arrive.

If single handle faucet has a bad cartridge, then faucet can have crossover.
Crossover means that cold water can enter the faucet even if faucet is turned to hot.
Bad single-handled faucet cartridge can delay or stop the arrival of hot water.
http://waterheatertimer.org/Crossover.html

Tankless require maintenance including cleaning combustion parts yearly, de-lime heat exchanger frequently, and clean water filter each month.
http://waterheatertimer.org/pdf/Tankless-maintenance.pdf
http://waterheatertimer.org/pdf/Bosch_Overcoming_fluctuating_temps.pdf
http://waterheatertimer.org/Troubleshoot-Rheem-Tankless-water-heater.html

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