Is the supplication "O He who saved Noah from the great distress, and saved Abraham from the blaze of the fire" authentic, and what is its full text?

The supplication mentioned has not been reported in an elevated Hadith (Marfu'), nor in a stopped (Mawquf) or cut-off (Maqtu') narration. There is no objection to seeking Allah's help in this manner. Allah Almighty has answered the prayers of His messengers and saved them from distress, as He says: "And [mention] Noah, when he cried out before [the flood], so We responded to him and saved him and his family from the great distress." It is better to supplicate with the reported (Ma'thur) prayers.