All perfect 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.
There is no sin in using the Olympic flame. Today, it is considered one of the practices through which the official opening of the Olympic Games is announced after it reaches the Olympic stadium. It is devoid of any religious or doctrinal significance.
Moreover, the prohibition mentioned in the Islamic texts regarding imitating non-Muslims is intended to prevent Muslims from adopting something that is a distinct characteristic of their beliefs or practices. However, actions that are general and not specifically associated with non-Muslims, nor related to their beliefs, are not considered imitation.
Similarly, what Imam Ibn Hajar mentioned about the use of red cushions (Miathir), which were mats made by non-Arabs and used as saddles on riding animals, often made from silk, is relevant here. He said: "If we say that the prohibition of using red Miathir was due to imitating non-Arabs, then that was for a religious reason, as it was their emblem when they were disbelievers. However, when it ceased to be specifically associated with them, that reasoning no longer applies, and thus the dislike for it is removed." [Fatih Al-Bari, vol. 10/pp.307].
He also commented on the hadith regarding Muslims wearing "Tayalis" (A type of scarf worn over the head, similar to what is commonly known as a shawl), which was originally a garment worn by Jews. He stated: "The story of the Jews only serves as valid evidence during the time when the Tayalis was specifically their emblem. However, that association has since disappeared, making it fall under the general category of permissible garments." [Fatih Al-Bari, vol. 10/pp.275]. This indicates that what was once a distinctive mark of non-Muslims is only prohibited as long as it remains their exclusive symbol. If it no longer holds that distinction, it returns to being permissible.
Therefore, there is no harm in using the Olympic flame as a symbol for the opening of sports games. This practice has become purely a sporting tradition, with no connection to beliefs or religions. And Allah The Almighty Knows Best.
