Use a piece of scrap fabric to stitch a small pouch for your lipoly battery. The pouch should be stitched to the back of the tie, just above where the Flora goes, and have an opening at the top for easy removal of the battery for charging. Use a seam ripper to open up the back seam of the tie just a little so you can thread the JST plug and wire inside the tie and down to the Flora.
The plug joins the Flora just inside the folds of the tie so it won't get caught on anything.
Tack your Flora in place with plain thread by stitching some unused pads to the tie. Try to just stitch to the back surface of the tie so the front fabric remains smooth.