Any of the titebond I II or III would work but the short acting (or slow) epoxy might be good if gap filling was needed. The key is cross grain so most glues other than epoxy are not doing much.
For interest. This is a partial account of an old article about Nakashima's tables etc. most were fairly thick.
"The butterfly key, used to edge-join two planks and to control actual or potential checks, has been known since Egyptian times. In Nakashima's shop, the butterfly tapers about 5 ° The bottom of the key is a hair smaller than the top, The recess is cut with an electric router about 3/4 of the way through and cleaned up with a sharp chisel. Then the key is glued and forced into place, with a single screw driven into each end from below for insurance. It's made about 3/16 in. proud of the surface, so it can be finished flush after the glue has set."