When I was checking my oil a 3/8 piece of plastic from the dipstick handle which seats into the oil dipstick receptacle broke off and fell into the oil. Can I drive my car without damaging the engine…if yes, for how long/how many miles? Or, should I have the oil system drained and flushed right away?
Don’t worry about it. This piece is too large to get sucked past the oil pick-up screen for the oil pump, and will probably just sit in the bottom of the oil pan. It may even fall out of the drain hole during the next oil change. I wouldn’t worry about it.
Thank you soooo much! I’m a pilot and know a little something about aircraft engines but not car engines 
Note that that piece of plastic may also hold the dipstick in the proper position in the oil pan. If the dipstick has slid either direction within that holder, or you can no longer tell exactly how far to push it in, you may now be getting erroneous oil level readings. I found that to be true on my C-170 that had C-172 engine installed. The oil level was actually two quarts lower in the tail dragger than it should have been simply due to the fluid seeking its own level.
A salvage yard will probably have a good dipstick.