What is minimum information required to identify if two people will be on the same flight?
Yes, Departure City + Flight Number + Departure Date will identify a single flight.

Where you may have a problem is if flight 123 goes from AAA to BBB to CCC to DDD on a particular day, and passenger 1 gets on flight 123 at AAA and flies all three segments, getting off at DDD, while passenger 2 gets on flight 123 at BBB and off at CCC.  To identify that those two are together on flight 123 departing BBB, you'd need to either have passenger 1 enter all the segments of his flight, even though he doesn't change planes at (nor even really much care about) BBB and CCC, or you'd need information about all the flights from some source, so that you know that "flight 123 from AAA to DDD" goes to BBB and CCC in between.