Andrew,
The pattern has to match exactly
d = DateObject[{"06/11/2019 10:55:44 AM", {"Month", "/", "Day", "/",
"Year", " ", "Hour12", ":", "Minute", ":", "Second", " ", "AMPM"}}];
DateString[d, "ISODateTime"]
(* 2019-06-11T10:55:44 *)
Change AM to PM
d = DateObject[{"06/11/2019 10:55:44 PM", {"Month", "/", "Day", "/",
"Year", " ", "Hour12", ":", "Minute", ":", "Second", " ",
"AMPM"}}];
DateString[d, "ISODateTime"]
(* 2019-06-11T22:55:44 *)