OS:RHEL5
DB:
SQL> SELECT * FROM V$VERSION;

BANNER
----------------------------------------------------------------
Oracle Database 10g Enterprise Edition Release 10.2.0.1.0 - Prod
PL/SQL Release 10.2.0.1.0 - Production
CORE    10.2.0.1.0      Production
TNS for Linux: Version 10.2.0.1.0 - Production
NLSRTL Version 10.2.0.1.0 - Production
SQL> alter database flashback on;
alter database flashback on
*
ERROR at line 1:
ORA-38759: Database must be mounted by only one instance and not open.

SQL> select open_mode from v$database;

OPEN_MODE
----------
READ WRITE

SQL> shutdown immediate;
Database closed.
Database dismounted.
ORACLE instance shut down.
SQL> startup mount;
ORACLE instance started.

Total System Global Area  285212672 bytes
Fixed Size                  1218968 bytes
Variable Size             125830760 bytes
Database Buffers          150994944 bytes
Redo Buffers                7168000 bytes
Database mounted.
SQL> alter database flashback on;
alter database flashback on
*
ERROR at line 1:
ORA-38706: Cannot turn on FLASHBACK DATABASE logging.
ORA-38707: Media recovery is not enabled.

SQL> alter database archivelog;

Database altered.

SQL> alter database flashback on;

Database altered.

SQL>

根据上面的错误提示和解决思路发现：
1、启动flashback时，数据库必须为加载状态，而不能打开。
2、要想启动flashback，必须先将数据库修改为归档模式。
目前只认识到这两点，大家有其他看法还请留言，以便共同进步。
由于本人对数据库了解不多，如理解错误还请帮忙指出，谢谢。