Praise be to Allah the Lord of the Worlds. May His peace and blessings be upon our Prophet Mohammad and upon all his family and companions.
It is prohibited to eat the flesh of the elephant, the snake and the frog:
As for the elephant, the prohibition is based on the fact that an elephant may use its tusks to attack other animals. Kindly check {Moghni Al-Mohtaj, V.6:149}. As for the frog, the Prophet (Peace be upon him) prohibited killing it and since you can`t eat it without killing it, you can`t kill it. Narrated AbdurRahman ibn Uthman: When a physician consulted the Prophet (Peace be upon him) about putting frogs in medicine, he forbade him to kill them." {Abu Dawoud}.
As for the snake, it is amongst the noxious creatures that the Prophet (Peace be upon him) commanded killing. Had it been eatable, he wouldn`t have called it a noxious creature, hadn`t ordered killing it, and hadn`t banned keeping it.
Al-Shirbini (May Allah have mercy on him) said: "Ordering the killing of these creatures and banning keeping them means that they have no sanctity. Had they been eatable, they would have been permissible to keep." {Moghni Al-Mohtahj, V.6:151}. And Allah the Almighty knows best.