The dry flowers are probably just finished blooming. They should be removed.
What kind of light are you giving it? It likes bright indirect light during the summer, so would prefer an eastern or western exposure during the summer. It needs more light, even full sun, during the winter, so you may need to move it to a southern exposure. Kalanchoes are members of the Crassulaceae family, and don't care for intense heat. For this reason, you will want to locate the plant in a sunny spot, but not up close to the glass of a window. Try to position the plant 6 to 12 inches back from the glass, to allow the air to circulate around the plant.
How much water do you give it? It's best to water it very thoroughly, then leave it alone until the soil is dry down to about an inch below the surface.
Other possibilities are that your plant is root bound, and needs to be moved to a larger pot, or that it is infested with some kind of insect. Mealy bugs and scale are particularly fond of Kalanchoes.
"Isn't it enough to see that a garden is beautiful without having to believe that there are fairies at the bottom of it too?" - Douglas Adams