如果你有兴趣使用windows函数。
选择*，lead（flag，success）over（order by name）作为表中的下一个\u comm；

SELECT *
FROM [Table_1]
WHERE [Table_1].id > (SELECT [Table_1].id FROM [Table_1] WHERE flag = 'success')
LIMIT 1

应在标记“success”后返回第一行

1） 我已经考虑了“id”列来考虑下一个记录

select * from yourtable where id = (select id from yourtable where flag='success')+1

或
2） 我也考虑过使用rownum

CREATE TABLE yourtable
    (`Name` varchar(3), `flag` varchar(7))
;

INSERT INTO yourtable
    (`Name`, `flag`)
VALUES
    ('ABC', 'fail'),
    ('DEF', 'fail'),
    ('GHI', 'success'),
    ('JKL', 'fail'),
    ('MNO', 'fail'),
    ('PQR', 'fail'),
    ('STU', 'fail')
;

create temporary  table t1 as 

select name,flag,@rownum:=@rownum+1 as rownum
from yourtable ,(SELECT @rownum := 0) as r;

select name,flag from t1 where rownum = 
(select rownum from t1 where flag='success')+1

在这里检查-http://sqlfiddle.com/#!2015年9月