While you CAN check a cooler as baggage, you cannot put any ice or dry ice in it, and frozen food may be challenged by the airline unless you are shipping it via air cargo.
It honestly is NOT a good idea to put frozen food in checked baggage, because if it goes astray or if there is a delay and it sits in the hold of a grounded plane on a runway for several hours, spoilage is inevitable, and the smell will spread to every other bag that is near it. I've seen several of these disasters, and they are NOT pretty. If you can get it into a carryon, that is the preferred way to transport it. (Remember the liquids ban, though -- no frozen soup, etc.)
However, if you are going to take the risk (and assuming that your airline has verified that you CAN check frozen food in baggage), here are the proper steps: Freeze the items in a deep-freeze for several days before departure, so that they are rock-hard. Pack each item in at least 2 layers of watertight packaging that is transparent. Line the interior of the cooler with a large heavy trash bag, and put a thick layer of absorbent material all around the frozen food INSIDE the trash bag, and also on top of the content where the lid of the cooler seam is. This will both add insulation and absorb any leaks. Leave the trash bag open until you have taken the cooler to the airline check-in counter and had it inspected. (Skycaps cannot take such bags; you have to go to the counter.) Once it has been weighed, inspected, and tagged, step to the side and seal the trash bag, tuck down the top insulation, and strap down the lid with at least two tight luggage straps. Then turn it over to the agent to go down the belt. The airline will mark it as having been inspected for disallowed contents, but TSA agents may open and check it anyway, so you don't want to use tape if you can avoid it.
The cooler top broke and it was taped with clear tape from the airport security, Hey the food was fine
