Slice the kumquats into thin slices horizontally across their equator, removing any seeds and setting them aside.
Wrap the seeds in a bit of cheesecloth, tie it up and place them in the jam pot.
Add in 3 cups of water and the sliced kumquats.
Allow the fruit and water to sit for 3-4 hours, so that some of the pectin can extract into the water (this step can be skipped for a slightly lower yield).
Turn on the pot and bring the mixture to a simmer. Cook for 35 to 45 minutes, adding a bit of water if necessary. At this point the jam should be starting to thicken.
Remove the packet of citrus seeds and add sugar.
Simmer the jam for another 5-10 minutes until the jam reaches gel stage (220 degrees F) or gels promptly when a bit is placed on a plate that's chilled in the freezer.
Funnel into prepared canning jars, remove air bubbles and apply 2 part canning lids.
Either store in the refrigerator for immediate use, or process in a water bath canner for 10 minutes to make the jam shelf stable.
Notes
I often choose to use less sugar, adding only 1/2 cup instead of the full 1 cup in this recipe. That makes a tarter jam, and lowers the yield slightly. Adjust to your preference.