fill the bottom flue tiles below the thimble or cleanout opening with lime. I like to install the clean-outs with quickrete polyurethane adhesive - in the masonry section at your local lowes - it's similar to expansion joint sealant for masonry, but perhaps a little stickier, I don't even screw them in anymore, that stuff won't let them move, and seals them perfectly.
Don't mortar the tiles tight to the chase above the thimble opening, use vermiculite and try not to let any mortar touch the flue unless necessary to hold it.
Tip for setting flues: lay them out before hand, take a square and check the ends. Of the four sides, mark the longest side as LL and the next longest side as L If it's square, mark it SQ on both sides that it's square on. Mark Both ends of the flue tile. (this is necessary because the flues are almost NEVER square cut on all four sides). When you're setting flues, check w/ level for plumbness, but, generally, by setting your LL's and L's on oposite sides of the preceding flue, you can keep the liner stack straight w/ out shimming.
when you get to the crown, make sure that you use sill seal around the flue, fill w. mortar between that and the precast crown. once the mortar dries, cut the protruding sill seal and caulk that space w/ same quickrete masonry adhesive sealant.