枯 is built from the 木 and 古 components.
It reads コ like 古, as do 個, 故, 固, and 居 — learn 古 once and the family's reading comes with it.
A common word using 枯 is 枯れる (かれる), meaning “to wither, to die (plant), to be blasted (plant)”.
Don't confuse it with 故, 固, 個, and 湖.