Oracle 11g Release 2

By using db<>fiddle, you agree to license everything you submit by Creative Commons CC0.

with tmp as (
    select 'username1' as username, to_date('2019-04-01 00:00','YYYY-MM-DD HH24:MI') as startdate, 1 as flag from dual union all
    select 'username1' as username, to_date('2019-04-01 01:00','YYYY-MM-DD HH24:MI') as startdate, 0 as flag  from dual union all
    select 'username1' as username, to_date('2019-04-01 02:00','YYYY-MM-DD HH24:MI') as startdate, 1 as flag  from dual union all
    select 'username1' as username, to_date('2019-04-01 03:00','YYYY-MM-DD HH24:MI') as startdate, 1 as flag  from dual union all
    select 'username1' as username, to_date('2019-04-01 04:00','YYYY-MM-DD HH24:MI') as startdate, 0 as flag  from dual union all
    select 'username1' as username, to_date('2019-04-02 05:00','YYYY-MM-DD HH24:MI') as startdate, 0 as flag  from dual union all
    select 'username1' as username, to_date('2019-04-02 01:00','YYYY-MM-DD HH24:MI') as startdate, 1 as flag  from dual union all
    select 'username1' as username, to_date('2019-04-02 02:00','YYYY-MM-DD HH24:MI') as startdate, 1 as flag  from dual union all
    select 'username1' as username, to_date('2019-04-02 03:00','YYYY-MM-DD HH24:MI') as startdate, 1 as flag  from dual union all
    select 'username1' as username, to_date('2019-04-02 04:00','YYYY-MM-DD HH24:MI') as startdate, 0 as flag  from dual
) 
select 
    tmp.*,
    dense_rank() over( order by startdate, username)-
     (case when flag=1 then
     row_number()over(partition by flag, username order by startdate, username) - flag
      else null end) as grp
      
    
from tmp
order by 
startdate, username

USERNAME	STARTDATE	FLAG	GRP
username1	01-APR-19	1	1
username1	01-APR-19	0	null
username1	01-APR-19	1	2
username1	01-APR-19	1	2
username1	01-APR-19	0	null
username1	02-APR-19	1	3
username1	02-APR-19	1	3
username1	02-APR-19	1	3
username1	02-APR-19	0	null
username1	02-APR-19	0	null