It's easiest to get started with this project if the flooring pieces are first cut into roughly 2-foot-long sections, so long as the rough cut width is wider than your desired width for the finished cutting board. Rip the flooring pieces. Each piece of flooring must be ripped twice.
If it's tongue-and-groove flooring, remove the "tongue" and "groove" from each piece with a rip cut on the table saw. Begin by running the flat groove side along the fence, cutting to remove the tongue.
It's fastest and easiest to rip the tongue side from all of the wood material before resetting the fence and moving on to the groove sides. After all tongues have been removed, you can reset the fence to rip off the old grooves from the opposite side of the stock.
Each piece of flooring will need to be planed flat on all four sides. Set the tabletop planer to the proper height and run material through the planer. Again, it's best to batch process a single side on all material at once before resetting and moving to another side. Plane the tops, bottom, left side and right side of each piece.
Using food-safe wood glue and nails, glue and nail every piece, making sure the joints are tight. It's best to do this on a flat, sturdy surface. It's important to allow the wood glue to cure fully before moving on to the next step.
Once the glue has dried fully, use a circular saw to rip one side of the butcher block straight (Image 1), then run it through the table saw to square the other edge (Image 2). For the edges, trim the butcher block with like material or another hardwood (Image 3).
Sand the top and edges using a belt sander and then an orbital sander. In each case, start with coarser grit moving toward fine. Once you've sanded to a smooth surface, wipe off the dust off and apply multiple coats of butcher-block oil or mineral oil to highlight the wood grain and provide a rich, finished look.