Does this sound like it would be a situation that homeowners insurance would cover?

Roof vents often leak. If it was a "one time" event and you have an all-risk (HO3) policy, it should be covered.

If water is coming in every time it rains and causing the decking or framing to rot, no it is not covered.

Coverage would not include repairing or replacing the defective vent installation regardless.

Most HO3 (standard) homeowners policies these days have strong limitations for water damage. Most have a 30 day discovery period - you must file the claim within 30 days of the water damage happening. It must not be a long term thing. You must have had NO reasonable belief that your roof was letting water in (ie, no visible water stains on walls or ceilings, no puddles, etc.) As the homeowner, you do have the responsibility to maintain your house, and prevent further damage.

You can't just let the water keep pouring in until the roof beams start to rot, and THEN file the claim. It's most likely NOT going to be covered.

The homeowners policy should cover the damage unless it is due to long term deteriation.

The flood insurance DOE NOT apply. You are not being flooded -- which means water coming from a river or lake.

You regualr insruacne MIGHT apply. CALL YOU INSURANCE AGENT

Usually water damage is only covered for sudden events. Read your policy. It will say.

No it is not accidental damage. You should have checked this on a regular basis. Negligence on your part.