B-G emerged as a rank title within the French armies of Louis XIV around the mid 17th Century and quickly spread amongst other European armies. I'm not sure that by the 19th Century B-G remained a substantive rank within the British Army but rather a temporary appointment, usually conferred on full Colonels for a specific posting, but occasionally conferred on ranks as low as Major. If this was the case, at the end of their appointment a B-G would revert to their former rank (unless promoted, of course).
I would expect there to be no greater probability of receiving a 'K' when B-G as any other officer rank. On retirement Colonels were often bumped to Honorary B-G.
In any event, B-G was replaced on 1st Jan 1921 with the two temporary ranks (appointments), Colonel-Commandant and Colonel on the Staff, titles that reflected the role more accurately. However these were themselves dispensed with in 1928, being replaced with the non-substantive rank of Brigadier. Around WW2 Brigadier became a substantive rank in its own right.
The Royal Marines retained two grades of Colonel-Commandant (in use since 1755) until the adoption of Brigadier in 1957. RM briefly flirted with B-G between 1915 and 1922.