I just found a picture of woolly aphids on an avocado branch:
If this is the case, look for individual insects something like:
When you pull the mass apart.
Aphids are easier to control than mealybugs, and you can simply apply a detergent solution, or spray with neem oil. Be sure you properly identify the pest before choosing a control method.
Older diagnosis, still a possibility:
Looks like a mealy bug infestation. You should confirm this before treating, by picking off some, and locating the insect bodies, which look like this. Yours seem to have quite a lot of 'cotton', which is common, but it hides the insects so identification from photo is more difficult. But I'm pretty sure by the groupings and placement that this is what you have.
There are several ways you can control them, but I use an isopropyl alcohol mixture, which dissolves the waxy coating, and then I treat with neem oil, which kills them. It's a one-two punch that has been around for some time. You can apply it with a paint brush or a cotton swab.
I've heard that a detergent solution will both dissolve the wax and kill the pest, but I fell that in that concentration, it's likely to leave burn marks on the leaves.
If you have a small infestation, one thing you can do :) is wipe them off with a damp cloth, and dispose of them. It's very simple, and works well, with a plant with thick, leathery leaves like a kumquat.