Thoroughly wash two quart-sized mason canning jars, lids, and rings in hot, soapy water and dry completely.
Evenly divide the green tomatoes, sliced onion, jalapeño discs, red pepper flakes, and minced garlic between the two jars, packing them tightly.
In a medium saucepan over medium-high heat, bring the distilled white vinegar to a full rolling boil.
Carefully pour the boiling vinegar over the packed vegetables in each jar, leaving a 1/4-inch headspace at the top.
Wipe the jar rims clean with a damp paper towel, apply the hot lids, and screw on the metal rings until fingertip tight.
Allow the jars to cool undisturbed on the counter until the lids pop and seal, then store in a cool spot for at least 7 days before opening.