COMBINE tomatoes, onions, garlic, hot pepper flakes, and celery seeds in a large stainless steel saucepan. Bring to a boil over high heat, stirring constantly. Reduce heat, cover, and boil gently until vegetables are soft, about 30 minutes.
TRANSFER mixture, working in batches, to a sieve placed over a glass or stainless steel bowl and press with the back of a spoon to extract all the liquid and pulp. This can also be done using a food mill. Discard solids.
RETURN liquid and pulp to saucepan. Add brown sugar, vinegar, lemon juice, salt, mace, mustard, ginger, and cinnamon. Return to a boil over medium-high heat, stirring occasionally. Reduce heat and boil gently, stirring frequently, until the mixture is thickened to the consistency of a thin commercial barbecue sauce, about 30 minutes.
PREPARE boiling water canner. Heat jars and lids in simmering water until ready for use. Do not boil. Set bands aside.
LADLE hot sauce into hot jars leaving 1/2 inch headspace. Remove air bubbles. Wipe rim. Center lid on jar. Apply the band until the fit is fingertip tight.
PROCESS jars in a boiling water canner for 20 minutes, adjusting for altitude. Remove jars and cool. Check lids for seal after 24 hours. The lid should not flex up and down when the center is pressed.