Can I cover a brick wall with wooden slats?

I am not really sure what you are trying to accomplish here with installing slats over the wall, I am not familiar with the look that you are seeking.   I will say that there is really not any easy ways to install the Slats on a brick wall.  With Concrete or brick using either Tap-Con masonry screws or a power actuated fastener gun could be a possibility, but neither would give a finished look.  You may want to find an interior decorator that can help you formalize your idea and maybe have another way to accomplish the look that you are seeking.