LOL. I hate airlines. I bet if you called again you would get different answers!! I was once flying back from the UK with hemerocallis. Since they were in bloom, I kept them with me. I had called the airline ahead of time, they assured me that there was no problem. I get to the airport and at the desk they tell me my plants are fine to go in the plane. Well, at security they threw up a stink because they were in soil,(nearly had to unpot them and wash the roots) and then once in the plane my plants were confiscated during take off and landing as they (and I quote) posed a threat to other passengers!
Oh, and when I flew home for xmas, I brought my mounted orchids with me since they need daily care. Security made me take the hooks off the mounts because they were considered dangerous! (but they didn't notice the bottle of water I forgot to take out of my backpack. Go figure.
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I don't think I would put the flasks in your checked baggage though, unless the seedlings are ready to be deflasked. Seeing how baggage handlers, well, mishandle baggage, you're going to end up with soup in the flask!