The dark ones are aphids, and the white ones are likely whitefly since they have wings. Since you have both then a careful search will probably turn up mealybugs as well since they are a known pest of Kalanchoe. These bugs are attacking the most susceptible parts of the plant, the fresh new growth and the flowers. Perhaps you have a source of these bugs on another plant nearby, maybe in a neighbour's garden.
One recommendation is to manually swab the leaf surfaces with cotton moistened with alcohol. That can be reasonably done with leaves but is much harder with the flowers because of all the nooks and crannies and closely packed flower parts. So if you decide to follow this route it might be best to clip off the flowers back to the stem, bury them in hot compost, and then focus entirely on the leaves. Do the leaf top surfaces first, then turn the plant in the pot upside down and do the same to the leaf undersides. May need repeat treatments.
The infestation looks quite advanced, so if you have more than one plant in the same condition consider composting these specimens and starting again with new; above all find the source of the infection and deal with that as well.