While I'm far from a chimney expert, we always use Thoroseal on that type of masonry product to seal it and fill the pores of the block. Makes for a great surface to paint to the color of your choice. It does not yield a slick surface but a textured one. Here's the website if you think this product will work for you.
In regards to the space/voids, 2" is more than you'll want to caulk. Might consider taking the asbestos siding down along side of it and running a 1x 6 trim down it and then reinstalling the siding. But it certainly appears to be asbestos siding in the pics so wear protective gear.