Hello Lennice- It is only covered if it is proved to be unuseable as a result of an insured loss/ occurence. If the furnace doesn't work because of basement flooding (and you have flood insurance specifically) then I think that replacing your furnace would be covered. If its just old age, use, neglected maintenance, wear and tear, then No.
Generally, with any insurance policy- you need to read the fine print. For every 1 page of what the policy covers, there are 3 pages for what it does not cover. Unfortunate, but the truth.
As far as 3rd party home warranties go, there are different levels of home warranties and different companies will cover different things and levels. And you'll have sometime an expensive deductible to pay for a homeowners warranty company to pick up the rest of the tab. And usually you will have to pay 100% of the bill, and then submit your bill to get some partial reimbursement from the H.O. warranty company.
Most warranties will have a pretty hefty "co-pay" like $1000 before they kick in.
Get 3 heating contractors to give you a written estimate- labor and materials.
Hope that helps. Good luck,