Is it permissible for an ordinary person to perform Ruqyah with the Quran on someone afflicted by Jinn possession, or does that pose a danger?

There is no harm for a Muslim in performing Ruqyah (exorcism/healing through Quranic recitation) for his brother with the Quran, even if the one performing Ruqyah is not a sheikh. The proof for this is the Prophet's (peace and blessings be upon him) saying: "Whoever among you can benefit his brother, let him do so." And whoever performs Ruqyah with the Quran may be antagonized by jinn and human devils; therefore, he must be diligent in reciting the authentically transmitted supplications for seeking refuge.