The following possibilities come to mind:

First, you could put a linear deck drain along one side. It may be that the slab is not perfectly level, and if not, put the drain on the downhill side.

Second, you could put a drain in. Using a core drill, drill a 4-6" hole in the slab. This is doable, I've done it, your local rental place will have a core drill. Then get a sharpshooter shovel and dig under the slab to the hole and install the drain.

Third, you could add slope to the floor by adding a thin layer of mortar/concrete whatever, in the same way that they would level a floor before laying tile. I'm not too familiar with this process, help from BW or someone?

Fourth, you could elevate the floor with stone, brick, block or other material.

Fifth, some combination of 1-4.

SB

we just built mine on a slab, it too drains to the back, which is good for me to wash and clean, i think a slight downgrade to the back is a good thing. we just nailguned our treated 2x6's to it and started building the alum frame from that. I bought a harbor frt. 10x12 and love it. The instructions were a little crazy but it can be done.....good luck

I'm not sure why you are worried about the concrete being level or draining. Are you worried about the sill rotting? Why not build a one block high foundation wall and put a 2x6 or 2x8 sill top of the blocks. Then build the walls on top of the sill. Be sure to put some foam stripping on top of the blocks and under the sill to help seal the cold weather out.