Who even said that... You're making implications based off my facts. I doubt the user could teleport part of his body, but why can't he teleport his clothes. Take Minato's quote for its full meaning, "As long as either I or my chakra are touching it, I can teleport it. " Obviously not the exact quote but you get the gist.
I agree on the part that Amatersau can be sensed and then a strong tier shinobi can block it or avoid its touch.
Not only Juubito but Edo Nagato was also able to sense it.
So it implies that any rinngan user or any highly skilled chakra sensor shinobi can sense the formation of amaterasu just before its release. While this is not the case with FTG.
Even Juubito was not able to sense FTG properly. But he could save himself or counter FTG once or twice using his stuff because of clone use with FTG. But against Minato & Tobirama's combined use of instanteneous FTG, even Juubito was stuck and got hit (of-course with help from Naruto/Sasuke).
Some members in the base like to argue that ameterasu is an instant jutsu. That, even if someone tried to FTG out of the way, he'd still be hit. I'm going to disprove that logic in this thread.
As we saw, ameterasu can be sensed, and blocked:
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"I sensed that you were focusing chakra in your left eye." ~ Obito Uchiha
Obito clearly says that.
Then we know, Tobirama is on the top 3 list of best sensors to live. He is so(let me make up a word here), sensorly inclined, that he could sense the make up of Orochimaru's body.
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"... His body is almost completely made of my brothers cells..." ~ Tobirama Senju
If he can see the make up of Orochimaru's body, surely he can sense chakra focusing in Sasuke's eye. I'm not going to sit here and compare Minato and Tobirama's sensing abilities, so I will merely say, Tobirama would be the one who can dodge ameterasu. Not Minato. However, if Minato's sensing abilities were on par with Tobirama, then of course he can.
Thus, it can be said FTG > Ameterasu spawning on you, as it can be sensed.
Now, onto, can FTG escape the eternal flames, or will they be transported with the users body. The answer, to me is obvious. The flames will merely fall to the ground. We've already deduced, as a community, that FTG enables the user to select, in their range of chakra, who, and what they want to transport. It would be foolish to believe the user would willingly teleport with ameterasu still on them.
This point has been proven over, and over again. Twice in this recent chapter alone:
1.
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"I'll have to jump with it!" ~ Minato Namikaze Minato is physically making the choice to use FTG with the explosive ball(due to lack of naming).
Again, we have another instance where the user chooses to FTG the ball.
2.
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"I'll return this to you" ~ Tobirama Senju
Tobirama chooses to teleport himself, and the explosive, and force it back into Juubito. He is physically holding the ball as well.
Conclusion:
1. FTG > Ameterasu if the user of FTG has an extreme proficiency in sensing, I.E; Tobirama.
2. FTG > Ameterasu even if the ameterasu is on the user. The user chooses, what and who to teleport with him.