How do I smoothly transition vinyl plank to tile?

You really have two general options for a "seamless" transition from tile to plank.

1. Basic "L" trim - pictured below. You will need to install this about 1/8" from each and caulk in between. It should be installed slightly LOWER than the height of the planks and tile - 1/16", 1/8" be OK. Your two floors must be pretty much exactly the same height or the "L" trim method will cause foot scrapes.

2. Bullnose trim - my general suggestion for most as it is more forgiving for slight height misalignments. Your planks will go into the bullnose and the tiles will be about 1/8-1/16" with a caulked gap.