What is a reasonable amount of time for an insurance company to take in settling a claim for a house fire that was a total loss?
There is no one-size fits all answer, since some claims require more investigation and some investigation simply takes longer. A house fire typically takes longer than most, since generally a fire dept. arson report is needed; there may have to be investigation of the insured, to see if he/she had any reason to set a fire (e.g. excessive debt that they needed insurance for, or a house underwater on value); and there are likely a lot of home furnishings, appliances, and possessions to both determine if it's credible that you had them and confirm the value of for claim purposes. At not-quite three months, in my experience for a house fire claim, this is starting to push what is acceptable, but is definitely not yet outside the bounds of what is reasonable--four to six months on a complex claim is not unheard of.
If it gets to the point that you are not wiling to wait any longer and believe they are simply dragging things out and refusng to pay, your recourse is to sue the insurer for "breach of contract"--for violating the contractual obligation (an insurance policy is a contract) to pay when the facts of the claim and terms of the policy require them to do so.