That looks like tacky weather sealing and little more. Unless there are serious cracks in the chimney, rather than just an airgap between the chimney and wall, there shouldn’t be any burning duct tape. If the duct tape burns, then so would the siding.
JD you are right there what usually happens is the fire place is built on a separate pad which has not been pinned to the house foundation and has little or no soil compaction, as a result it just starts to tilt away from the house over the years, or if the mortar joints don’t dissolve first and the whole damn thing just falls down in a wind storm
foil tape is designed for SMOOTH SURFACES (duct work preferable clean)so the porosity of brick and the tweaked siding won’t let that fix last long at all
not many times where caulk (siliconized LATEX)is the best solution but this might be one and a foam rope packing first inserted would minimize the total amount of caulk needed to say 1 case insted of 3