Well if we are being competitive, I am missing only three in captivity - Asian Open-billed, Jabiru and Greater Adjutant. Plus have seen two species wild and another two feral (zoo escapees from Singapore).
But I haven't seen the Black-necked Stork wild, so need to get to Cairns!
I completed my full set of captive storks with Greater Adjutant at Saigon Zoo in 2012. I've seen (slightly to my own surprise) 9 stork species in the wild.
I'm joint first on wild storks with nine species wild:
Marabou
Yellow-billed Stork
Asian Openbill
African Openbill
Abdim's Stork
African Woolly-neck
White Stork
Black-necked Stork
Saddlebill Stork
And captive I have seen:
Abdim’s Stork
African Open-bill Stork
Asian Woolly-necked Stork
Black-necked Stork
Black Stork
European White Stork
Marabou
Oriental White Stork
Saddlebill Stork
Yellow-billed Stork
Lesser Adjutant
Storm’s Stork
Maguari Stork
Which in total is 15/20 if Woolly-necked is split or 14/19 if not.