The black king will do fine under the same requirements as your corns. Same setup, same temps, same food!! Should do just fine. Regarding the king snakes in general, the majority of lampropeltis getula can be kept the same as any of the elaphe obsoleta/guttatta complex.
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RATS
1.0 Corn snake "Warpath"(KY locale)
1.0 Black rat snake "Havok" (KY locale)
1.1 Black rat snakes "Reaper and Mystique" (MO locale)
1.0 Albino Black rat snake "Malakai" (Dwight Good stock)
1.0 Everglades rat snake "Deadpool" (Dwight Good stock)
0.1 Greenish rat snake "Rogue" (Dwight Good stock)
1.0 Great plains rat snake "Reign Fire" (TX locale)
1.0 Grey rat snake "Punisher" (White oak phase)(Dwight Good stock)
RACERS
1.0 Eastern Yellow Belly racer "Nightcrawler" (MO locale)
KINGS
1.1 California king snake "Bandit" & "Moonstar" (Coastal phase)
1.1 Prairie king snakes "Bishop" & "Askani" (KY locale)
0.1 Black king snake "Domino" (KY locale)
1.1 Desert Kingsnakes "Gambit" & "Psylocke"
0.1 Florida Kingsnake "Shard"
0.1 Speckled Kingsnake "Haven"
MILKS
1.0 Eastern/red Milk intergrade "Cable" (KY locale)
1.0 Eastern/Red Milk intergrade "Omega Red" (KY locale)
BULLS/GOPHERS/PINES
0.1 Sonoran Gopher "Husk"
1.0 Kankakee bull (Phil Peak stock)
Good luck and Happy Herping
Brian