For my rental property, I hired a contractor for renovation (new flooring and paint). When claiming capital cost allowance, under which class would they fall?

If the new floor that you installed is the same as or similar to what was originally there, this would be a current expense, and you would just claim the whole amount in one year.

If the new floor is substantially nicer than the old flooring you might be able to consider it a capital expense. In that case you would either add it to the CCA class of your building or put it in Class 8 (misc items).

Same for the paint job.