What the contractor should have done was flush the new pipe BEFORE connecting it to the house's internal plumbing. If the contractor is reluctant to come and fix his mistake, you should call him tomorrow mid-morning and tell him that you have been in contact with an attorney and that he will be responsible for any damages caused by his malpractice. Also, he will be sued for actual and compensatory damages if anyone in your household gets ill from bacteria introduced into your piping. Tell him that Legionnaires Disease has a long incubation time and infections can be fatal. That might light a fire under his butt.
The night before flushing your pipes, set the thermostat on your water heater to "Pilot"; no need to turn it off.
Continue with the rest the next day...
Do you have a pressure regulator on your water supply? If you do, it would be best to bypass it to flush your lines. But that's probably beyond your skills, so the next best thing would be to adust it to max pressure. Using a sharpie, put a mark on the top of the cap screw. Using a wrench, release the locknut and then turn the adjusting screw clockwise into the valve as far as it will easily go (do not force it). Referencing your mark, count the number of turns until you stop. To restore your original pressure setting after you've flushed your pipes, reverse the same number of turns until the mark is in the original orientation. This should get you close enough. If you want the pressure to be accurate, you will have to buy a water pressure gauge at your local hardware store (~$10) to reset the pressure.
I would start flushing by finding an outdoor spigot (garden hose connection) outside the house closest to where the water supply enters the house. By now, you can be sure that sediment has already been distributed through all your pipes. But there's no point in distributing more if there's still dirt in the water main between the meter and the house. Open that spigot 100% and let the water flow fast for a couple of minutes.
Next, go to the other hose spigots around the house, opening them in turn. Hopefully, each will help flush different sections of piping in your house.
Next, go to any bathtub inside the house, starting with the one closest to where the water supply enters the home (first floor before the second floor). Open each of these 100%, cold then hot one at a time, and fill half the bath with water. Repeat for every tub. If a bathroom only has a shower, remove the showerhead and turn the showerhead on 100%, cold then hot one at a time, and run for a couple of minutes.
By now, your water heater should be sufficiently cooled. Connect a drain hose to the drain on your heater and flush several minutes until the water runs clear.
Finally, you should flush the kitchen sink lines specifically since you already know they contain dirt (the sink was probably turned on first after the pipes were replaced). Get a long flexible supply line that matches the supply stop valve connection. Shut off your supply stops and disconnect the supply line to the faucet (one at a time). Connect the spare line and put the end in a 5-gal bucket and open the supply stop 100%. Fill the 5-gal bucket about half full. Remove the spare line and reconnect the supply line to the faucet. Repeat with the other stop valve. Now remove the aerator from the faucet, disassemble, clean, reassemble, and replace. Test your faucet. If still slow, you will need to shut off the supply stop valves, remove the faucet valve cartridge and clean it.
The best way to sanitize your pipes is with chlorine bleach. But that's beyond the scope of this post. What you can do is a high temp sanitization of your hot water pipes (which are more susceptible to bacteria growth than the cold water pipes).
Turn your water heater up to 160 deg. THIS IS DANGEROUSLY HOT AND WILL CAUSE IMMEDIATE BURNS -- DO NOT DO THIS WHILE YOU HAVE YOUNG CHILDREN IN THE HOUSE. After the water heater reaches full temperature, run hot water at every fixture in the house until the water is 160 deg coming out of the fixture. BE CAREFUL NOT TO GET SPLASHED WITH THIS VERY HOT WATER. Start with the fixtures closest to the heater and work your way to the one farthest from the heater. Do every sink, shower, tub, etc. Run the dishwasher and laundry washing machine on a hot cycle. You will have to wait for the water heater to recover after doing each fixture. After doing this, wait an hour. Then turn your water heater thermostat down to its normal setting. THE WATER WILL STILL BE DANGEROUSLY HOT FOR A WHILE. Do a load of laundry on hot or warm to bring the temperature down faster.