A B♭ Major 6 (B♭6) chord contains the notes A#, F, D, G. It is built from the major 6th formula 1 - 3 - 5 - 6, with Bb as the root.
How do I stop the flattened ring finger from buzzing?
Roll the finger slightly onto its side rather than pressing flat with the pad, and keep it close behind the fret. The joint creases are what usually deaden a string, and rolling moves them off the strings. It's the same technique that makes a full barre chord ring, applied to four strings instead of six.