There are two ways that anyone can determine the amount of delay - a screen shot of US' flight status page and BTS reports (part of the DOT). The first is only available for a specific flight for a limited time and the second is only available after 2 - 3 month's delay.

FlightAware gives from real-time to historic departure and arrival times. You can sign up for free and get a longer period of historical arrival and departure times.

It would seem that the insurance carrier wants something from the airline showing not just the delay but possibly also that the rebooking was required. While the delay is relatively easy to prove, assuming they accept any of the above as proof, it's going to be hard to come up with documentation for since the need for rebooking depends on an individual's circumstances.

Jim