After the cars engine has started there is a screeching noise for roughly 6 seconds then it stops
My car has 140000 miles.
Assuming that it is not an electrical issue (e.g. somehow power is NOT being cut once you release the key from the "start" position) you have a mechanical flaw with the starter. It is hard to say from your description if the noise is merely "internal" to the starter or it is due to the starter being temporarily still entrained in the flywheel ring gear once car has already started.
If it is the latter issue, you may be damaging the flywheel and should not use the car until this issue is repaired (flywheels are very difficult to replace). Overall, my guess is you need a new starter motor. A certified technician from YourMechanic can help with sourcing the correct part and can install the a new starter at your home or location of the car.
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