Instead of subtracting sensitive information, it may be more straightforward to start with nothing and add non-sensitive information. In general, if you provide the (departure) date, airline, and flight number, that should be enough for anyone to look up the time, duration, both airports, gate, and terminal, as well as check for delays (e.g. by putting the airline and flight number into Google). Some flights consist of multiple segments, so you may also need to indicate which segment you're talking about. Depending on your situation, you might also want to tell them your name, seat assignment, cabin class, or any other personal information which they legitimately need to know.
In general, there is no good reason to provide anyone with your booking code or confirmation number (or whatever your airline calls it). The only purpose of this code is to check-in, rebook, cancel, or otherwise mess with your flight, and nobody besides you should be doing any of those things. If anyone asks you for this code, you should refuse to give it to them unless they are affiliated with the airline or your travel/booking agency.