Is saying Sadaqa Allah Al Adhim is a Bida' or not, please give proof.

Praise be to Allah, the Lord of the Worlds; and blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.
No doubt, Allah is the most truthful of all. Allah Says (interpretation of meaning): {and whose words can be truer than those of Allâh? (Of course, none).}[4:122]
The fact that a person says: "Allah The Great is Right", "Sadaqallah-ul-Atheem" is an absolute expression which should not be limited to a given time, place or situation without a clear evidence to do that. So, since habitually saying this expression anytime one finishes reading the Qur'an or listening to it is not supported by any legal evidence, it is not permissible to do it.
If one says it as a form of worship this is unlawful as there should not be any innovation in worship. If the person wants to conclude a reading in the best way, he should just remain silent. The Prophet once listened to Abdullah Ibn Massoud reading the Qur'an and when he wanted him to end his reading he said to him "That is enough". [Reported by Imam Al Bukhari]
The Muslim should look to the Sunnah and abide by it instead of sticking to some innovated expressions or sayings which were not reported from the Prophet. Such expressions might become so widely used and so common that people take them as Sunnah. So, if the pupils and students grow up repeating this expression after reading any verse of the Qur'an then, they would think that it is Sunnah while it is not.

Allah knows best.