the way they formulate this sentence makes it a bit ambiguous. it could mean early as well as soon. "họ sẽ sớm có một chuyến bay" would undoubtedly be "they will have a flight soon". and adding sáng to sớm would make it clear that's early in the morning, "họ sẽ có một chuyến bay sáng sớm".

That's also what I was thinking for this sentence.