You can see all the flights for a single carrier on a particular route, but not all flights. Select the advanced option on the Flight Tracker. Type in the airport names or codes for the departure and arrival airports, pick an airline and specify the departure date you want to use for the search. You'll see a list of all flights on that date connecting between those two airports. If you see a flight you want to track, click on the flight number for detailed status information.
If you are using our paid historical flight status tool, you do not have to specify an airline when searching a route.