With regards to this issue, Dr. Marawan Shahin, Professor of Hadith and its Sciences said:

“If the animal has been slaughtered by a Christian or Jewish and the animal was slaughtered while alive but one is not sure if they have mentioned Allah’s name while slaughtering it, it is permissible for a Muslim to mention Allah’s name and eat from it. But if the animal was slaughtered by a person who does not belong to the People of the Book i.e. a Jew or Christian, or the animal was not alive when it was slaughtered, then it is not permissible for a Muslim to eat from it. One more condition is that the animal should be halal in the first place.”

As for kosher products, they are considered halal only if they are free of any haram ingredients. Elaborating on the Islamic ruling on eating kosher meals,Sheikh Ahmad Kutty, an Islamic scholar said the following:

“Kosher products are halal only if they are free of ingredients that are considered haram, for it is not uncommon for even the foods served in hospitals as kosher foods to contain wine. Hence, even though these foods may be labeled kosher, they cannot be deemed halal for us to consume, because they contain wine.

Therefore, not all kosher products are halal.
Meanwhile, halal products are strictly made up of halal ingredients by the very definition of them.”