There are two general approaches for joining flat brick stitch beadwork. I refer to them as the Aligned Beads Techniques and the Offset Beads Technique.
Aligned Beads Technique
With the first approach, the beads in the two rows being joined are aligned vertically. This is different from the normal alignment of brick stitch rows, where the beads are offset like bricks in a wall. To make the join, follow the path of the thread shown in the diagram (in dark brown) above. Notice that this is a variation of square stitch, or of a basic sewing back stitch.
Offset Beads Technique
With the second method for joining flat brick stitch, the beads in the two joined rows are offset. This creates a less noticeable join than the Aligned Beads Technique, because the beads are aligned as they would be in contiguous rows of brick stitch.
To make this join, use the thread path shown in the diagram (in dark brown) below. Notice that you wrap the thread from one row around the bridges of thread in the other row, just like you do when stitching regular brick stitch.