FEMA says it plainly: "Most homeowners insurance does not cover flood damage."
Rising water from a storm, a river or a flooded street is flood. A homeowners policy is written for other things: a burst pipe, a fire, wind that tears off the roof and lets rain in. When Gulf water or bayou water comes in under the door, the homeowners policy is usually not the one that pays.
Flood coverage is a separate policy. FEMA’s National Flood Insurance Program sells it in participating communities; in FEMA’s words, it "is available to anyone living in one of the 22,600 participating NFIP communities," and it "can cover buildings, the contents in a building, or both." Those are two separate choices. A policy on the building alone will not pay for the couch, the clothes or the freezer.
FEMA notes that homes in high risk areas with government backed mortgages must carry flood insurance. If you are in Zone X, nobody will require it, and that is exactly where many uninsured flood losses happen. Hurricane wind and named storm deductibles are a different subject, covered on our page about hurricane deductibles and the Beach Plan.
The 30 day wait
FEMA’s own wording: "Typically, there’s a 30-day waiting period from date of purchase before your policy goes into effect." FEMA lists a few exceptions on the same page. For most homeowners, a policy bought when a storm is named in the Gulf will not be in force when it arrives. June is the time to buy, not September.