What is the ruling on a father's permission being a condition for his daughter to slaughter a chicken, and does this have a sound basis?

There is no basis for the condition of the father's permission for his daughter to slaughter. This is from the sayings of common people, and scholars have not mentioned it among the conditions for the slaughterer. The necessary conditions that must be met by the slaughterer for his slaughtered animal to be lawful are: that he be sane and discerning, a Muslim or a person of the Book, that he intends the slaughter, that the slaughter not be for other than Allah, that he not mention any name other than Allah's over it, and that he mention Allah's name over it. Furthermore, it must be lawful if he slaughters wild game.