Yes condoms can sometimes cause a burning sensation inside a woman's vagina.
Most commonly the condoms such as those condoms that are scented, flavored or those condoms that contain spermicide can cause irritation and a burning sensation in the vagina.
Older condoms that are drying out can also lead to a burning sensation in the woman's vagina and have the potential to break and then cause unwanted pregnancy.
If the woman is experiencing a burning sensation from the condoms then you may need to switch condoms and if you're using scented or flavored condoms then you may need to switch to regular condoms.
The woman may also have an allergy to the material the condom is made from as well.
Some men also experience a burning sensation on their penis or other irritation from certain condoms which may mean the man has an allergy to the condom as well.