First what I said in my comments is my own opinion and interpretation. The answer based on fatwas is clearly that it is a bida'h as it was not reported by anybody that the Messenger of Allah () nor any of his sahaba did so. This is the view of the fiqh council of Saudi-Arabia, of Sheikh al-Barak and ibn 'Othaymeen:
The Standing Committee for Issuing Fatwas was asked: Did the Prophet (blessings and peace of Allah be upon him) recite al-Faatihah after offering supplication?
They replied: There is no proof that the Prophet (blessings and peace of Allah be upon him) used to recite al-Faatihah after offering supplication, as far as we know. Hence reciting it after offering supplication is an innovation. And Allah is the source of strength.
End quote from Fataawa al-Lajnah ad-Daa’imah (vol. 1, 2/528)
But the practice to end a du'a which is reported to us is different for example some ahadith recommend to end a supplication by praising and thanking Allah and sending prayers to his Prophet. This is the same way we are asked to start a du’a as you may read in ahadith like this, this. Also have in mind verses of the Quran like.
And to Allah belong the best names, so invoke Him by them. ... (7:180)
... And the last of their call will be, "Praise to Allah , Lord of the worlds!" (10:10)
or the hadith which is considered as weak by some scholars which Imam al-Bayhaqi has quoted in his sho'ab al-Iman:
عن جابر بن عبد الله رضي الله عنهما، قال: قال رسول الله صلى الله عليه وسلم: لا تجعلوني كقدح الراكب، فإن الراكب إذا أراد أن ينطلق علق معالقه، وملأ قدحا ماء، فإذا كانت له حاجة في أن يتوضأ توضأ، وأن يشرب شرب، وإلا اهراق، فاجعلوني في وسط الدعاء وفي أوله وفي آخره.
Where our Messenger asks and recommends us to send prayers and blessings upon him in the middle and end of the supplication.
See also this fatwa in English and this in Arabic on the matter of fatiha and this fatwa in English about the etiquette of making dua'.
So if we teach others how to supplicate the right way we can do this "in congregation" as this is a dark or grey zone of jurisprudence where we might be safe from committing an innovation in the religion. But we shouldn't declare something which has never been made -in the early centuries- as fine or as a good deed. The fatiha itself is a kind of dua' and it consists of many points which are part of the etiquette of doing supplication, but ending a supplication with it has a touch of bida'h even according a not that strict view as the salafi PoV.