All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
Saying Ameen after a supplication (Dou'aa’) said by someone else is not a form of Shirk. The Prophet ordered Muslims to say Ameen along with the Ameen that the Imam says in prayer. The Prophet said: “When the Imam says Ameen, say Ameen.” [Al-Bukhari]
It is also confirmed that the angels say ‘Ameen’ to our supplication as reported by Al-Bukhari. The Prophet said: “When the Imam leading the prayer says Ameen, say Ameen. In fact, anyone whose Ameen coincides with the Ameen of the angels, all his previous sins are forgiven.”
Muslim reported that the Prophet said: “Whoever makes a supplication for his brother without the latter's knowledge, the angel in charge of that says: “Ameen and for you the same.”
So, saying Ameen as a follow up to a supplication chorally is not a form of Shirk as your friend claimed.
For more benefit, please refer to Fataawa 192681, 272407, 84069, 93593, and 89938.
Allah knows best.