I've experienced probably 1 to 3 flats on the road every year for 30 years and never been anywhere near losing control because of it. Typically I just notice a "thunk thunk" sound and maybe a "thunk thunk" feel as the valve area of the flat tire hits the road repeatedly. If you have a blowout, a noise like a gunshot may make you jump, but once you recover from the noise, it's no different than any other flat. Just put on the brakes and slow down, stop and change the tire. The majority of my flats have been on sew-ups, so that's a little different feel, and also safer to ride on when flat. The major concerns with flatting are that if you are cornering with a strong lean and a tire suddenly goes flat, you may have rim in contact with the road rather than rubber and the wheel would slide out from under you. If it's a rear tire, you go down and take some road rash. A front flat under those conditions could be worse. At high speed, you need to be careful how you use the brakes with a flat tire. Try to use the brake on the non-flat wheel only, because a flat clincher tire can slide around the rim when the brake is put on.
Oil is good, grease is better.
2007 Peter Mooney w/S&S couplers/Terry Butterfly
1993 Bridgestone MB-3/Avocet O2 Air 40W
1980 Columbus Frame with 1970 Campy parts
1954 Raleigh 3-speed/Brooks B72