What kind of grill are you using? You say charcoal, so is it a Weber kettle or another domed type grill? The design of the dome grills prohibit flare ups while the lid is on.
If it is a square type grill, or an open pit, you’re likely to have some problems with fatty meat like burgers and chicken quarters.
For you patties, just work them really well so that the meat is pressed together good. You don’t want to be able to see the individual shreds of meat, but instead want a homogeneous patty. If it’s loose and you can see the individual strands, it’s liable to break apart.
Don’t worry about greasing the grate. When your coals are ready, spread them and put the grate on and allow it to heat for 5 or so minutes. Drop the patties on the hot grate, and then cover the grill. A good sear and the fat from the burgers will cause them to naturally release when they are ready to flip......about 5 minutes of cooking.
Flip them, then cover and cook another 5. When you flip them, it often helps to move them around to a different spot if they are real fatty. The fats can drop down and cool the coals directly under the patty (but that is likely to flare up when the lid comes off), and moving the patties to another spot where the grate is hot allows a good sear on the second side.
When you lift the lid, depending on your coals and grill, it is liable to flare up...big time in some cases. Don’t sweat it. Just flip your burgers and cover the grill again. Once the lid is on, the flare up will die down. However, this only applies to a domed grill. If you’re using a square or open pit (or a gas grill for that matter) you’ll want to move the patties to an entirely new location where the fat hasn’t dripped down yet.
After 5 minutes on the second side, depending on the size of your burgers, you’re done or nearly done. Press lightly on the burger (don’t mash on it as this will squeeze out the juices), and see if it’s firm. If it is thick and feels squishy like a water bed, it’s not done. A meat thermometer is your best friend at this point if you aren’t used to judging doneness by feel. If they need a little more time to fully cook, flip them again, and let them cook a few more minutes.