The general principle related to eating the meat of slaughtered animals of the people of divine scriptures is permissibility. God Almighty says in the Quran, “This day [all] good foods have been made lawful, and the food of those who were given the Scripture is lawful for you and your food is lawful for them” (Quran 5: 5).
It is permissible to eat from the food of the people of the Book, Christians and Jews. It is likewise permissible for you to eat the chicken they offer without ascertaining the means of its slaughter as these animals are either slaughtered mechanically or manually by either a Muslim or by a person from the people of the Book. When it comes to meat, the same ruling applies except that you just need to make sure it is not pork as it is prohibited in Islamic law.
It is lawful for you to eat any kind of meat except for pork without exhausting yourself with further investigation and scrutiny.

And God Almighty knows best.