First Solution: TSQL in the SOURCE sql command.
I use the temp table, change the table name accordingly please. Tested, works perfect in SSIS. :)
--create table structure
create table #test (strg varchar(1000))
go
--insert into sample data
insert #test values ('"v" : {"cns":"AQRV3Z","elapsed-ms":"1","key-hash":"377515780","key-size-b":"116","load-time-ms":"250","lower-bound-ms":"20","outcome":"done","value-size-b":"3124"}')
--below is solution for the data source
select substring( strg,
charindex('"load-time-ms"',strg)+len('"load-time-ms"')+2,
charindex( '"',
substring( strg,
charindex('"load-time-ms"',strg)+len('"load-time-ms"')+2,
len(strg)))-1) as [col1-load time],
substring( strg,
charindex('"outcome"',strg)+len('"outcome"')+2,
charindex( '"',
substring( strg,
charindex('"outcome"',strg)+len('"outcome"')+2,
len(strg)))-1) as [col2-outcome]
from #test
RESULT:
In SSMS:

In SSIS:



Second Solution: Derived column in SSIS, tested, works perfect. :)
col1-load-time
SUBSTRING(strg,FINDSTRING(strg,"\"load-time-ms\"",1) + LEN("\"load-time-ms\"") + 2,FINDSTRING(SUBSTRING(strg,FINDSTRING(strg,"\"load-time-ms\"",1) + LEN("\"load-time-ms\"") + 2,LEN(strg)),"\"",1) - 1)
col2-outcome
SUBSTRING(strg,FINDSTRING(strg,"\"outcome\"",1) + LEN("\"outcome\"") + 2,FINDSTRING(SUBSTRING(strg,FINDSTRING(strg,"\"outcome\"",1) + LEN("\"outcome\"") + 2,LEN(strg)),"\"",1) - 1)