Here's how I'd approach it if I were you:

* Review a list of airlines that operate a particular type of aircraft (Wikipedia's list of A340 operators here)
* Determine which operate on the route you're flying (in the case of the A340, none because none are US-based airlines and foreign airlines cannot operate domestic US flights)
* Then go to the airline's website to see if you can determine what airlines are typically used on that route, or what routes a plane is typically used.

Of the 777 operators, America, Delta and United are the only US carriers. You can then drill down on each of their sites to see your flight options.

ETA: You can also search things like "AA 777 routes" and your first Google result will be a page on AA's website describing it as their flagship international plane, which also clues you in to the fact it's not typically flown on domestic routes.