Of course you should never leave any open flame unattended. It takes mere moments for flare ups to run out of control. By the time you walk inside the house to get a beverage in the refrigerator you could have a blaze on the kettle grill.
First, if you expect dripping oil or any pooling grease at all consider using a drip pan and an indirect heat source (off set flame or coals) before you cook.
Place a sturdy aluminum pan filled with water (juice or beer may be nice) under the grate beneath the meat or drips. This will avoid major flare ups and protect succulent meats from over cooking. Indirect heat like this is usually desired for cuts thicker than the palm of your hand.
Second, make sure you start with a clean grill. A dirty grill can mean pooling oil and grease that can ultimately flare up.
Third, have a dry chemical fire extinguisher handy whenever grilling. It’s O.K. to use the one temporarily from the kitchen (you DO have one in your kitchen right)? Baking soda can also be used to stop a small grease fire. You may need a lot (and baking flour!)
Fourth, NEVER spray water on a grease fire. It will most likely flare up and spread.
Fifth, In the kitchen you can often cover a grease fire with a pan lid. to cut off oxygen. This is very difficult on a grill grate. A heavy wool or flame retardant blanket can sometimes smother a flame.
And finally do not try to move the flaming material. Turn off the burners and if all else fails get away and call 911.
Flare ups can be a real danger with live fire cooking. Keep charcoal grills off wood decks and all grills clear of vinyl siding. In fact its good practice to remove any and all flammable material at least ten feet away from active and hot grills and barbecues. This includes the ground (dry grass can catch fire in an instant in the dry summer months). Use some advance planning and keep it safe.