フライトが恋しいです
Hilarious. That’s “I missed my flight” in the same sense that “I missed my wife (but she’s back from her trip now).” As in, “I long to be with my flight, but alas, we are apart.” See: https://jisho.org/word/%E6%81%8B%E3%81%97%E3%81%84
飛行機に乗り遅れました
This would probably be the translation I would use. I’m surprised that it’s not directly in the corpus as a canned phrase. In this phrase, 乗り遅れました literally means something like “[I] was too late to board [the plane]” and doesn’t express some kind of bizarre longing or affection for the plane.