Burning Bakhoor / Oud while fasting

In principle, it is permissible to burn oud or bakhoor while fasting. This does not affect the fast.

However, one must abstain from intentionally inhaling the smoke of the incense while fasting. This normally occurs if one places his face above the burner and thus directly inhales the smoke. If one intentionally inhales the smoke while fasting, the fast will break and Qadha will be compulsory. (Shaami 2/395)

And Allah Ta’ala Knows Best