Prepare the jars and rings by washing on the hot cycle of your dishwasher. Wash the lids in hot soapy water and rinse well. Place in a bowl covered by two or three inches of very hot tap water. Set aside.
Prepare your canner (or stockpot) by putting a rack in the bottom to hold the jars away from the base of the pan. If you do not have a rack, use a fully opened vegetable steamer basket or extra rings from 'regular-mouth' or 'narrow-mouth' canning jars placed facing down with the sides touching. Set aside.
Sprinkle salt over the minced garlic in a metal or glass bowl (don't use plastic here unless you want a perma-garlic bowl!) Stir together, cover tightly with plastic wrap and let it mellow at room temperature for an hour. The salt will help pull some of the moisture from the garlic, so don't skip this step!
In a saucepan, bring the vinegar to a rolling boil. Add the sugar all at once and stir well until the sugar is dissolved. Return to a full boil. Lower heat just slightly so that it boils steadily but not really hard. Boil steadily, uncovered, for 10 minutes. Remove the pan from the hot burner, stir in the garlic mixture and the crushed red pepper flakes. Take care not to hold your face directly over the pan when adding in the pepper flakes as that can trigger some serious coughing and eye-watering, depending on the strength of the pepper flakes.
Ladle the hot sauce into the hot jars. You want to leave 1/2" of space between the top lip of the jar and the top level of the dipping sauce. Use a ruler outside the jar to check whether you have the right amount of open space. If you need to, use a spoon to remove some sauce or add sauce to maintain that 1/2" of headspace. Use a paper towel (or clean tea towel) dipped in pure cider vinegar to wipe the rims of the jars even if it doesn't look like anything is on it.
Use your clean hands to grab a lid from the hot tap water. Position it, rubber seal side down, directly over the center of the jar. Place the metal ring over the jar and gently screw it into place until you meet resistance. When you meet resistance, tighten the jar until it is finger-tip tight. (In other words, tighten until it is the tightness that you can achieve with your finger-tips, not with vice-grips.) The jars are going to be hot because you poured nearly boiling liquid into them. I find it helpful to wear an oven mitt on the hand that is holding the jar steady.
When all of your jars are ready, set the prepared canner on your burner. Position the jars (using an oven mitt to keep from burning your fingers or palms) over the rack (or steamer basket or upside-down canning lids) so that the jars are steady and in an upright position. Cover the jars completely by at least one inch with hot tap water. Place a lid on your canner (or stockpot) and turn the heat on your burner to high. When the water reaches a full, rolling boil (one that could not be stirred down), set your timer for 15 minutes. When the 15 minutes have elapsed, remove the lid to your canner and shut off the heat. Leave the jars in the hot water for 5 minutes.
After 5 minutes, transfer the jars (using a waterproof oven mitt or canning tongs) to a towel lined counter or a cooling rack with a towel under it. You should start to hear the "POP" of the lids as they form vacuums and seal. This is a very good thing! Leave your jars to rest, undisturbed, overnight. In the morning, test the jars by pressing gently on the center of each lid. If it does not give under gentle pressure or pop back up, your seal is good. Remove the rings for storage*, wipe gently with a damp cloth or paper towel, label and store in a cool, dark place for 3 weeks prior to using. Unopened, sealed jars of this sauce can be stored for a year.
*Storing your jars without the rings is a little bit of insurance. When food spoils in a closed environment, the gasses produced by bacterial growth create upward pressure in the air pocket left by the headspace you so carefully measured in the jar. If you remove the ring, any gasses produced by spoilage will push upward on the lid loosening the seal. When you open a jar, if the seal is weak or there is no "schllllllooop" from a vacuum seal being broken, discard the contents immediately. On the flip side, if you hear that lovely "schllllllllooop" and the lid is difficult to pry from the jar, you've done the job right! You can eat your home-canned goodies, content in your foodstuffs' safety.