I am interested to know what other databases have features similar to Oracle's Flashback Query. It would seem that any database that supports MVCC could have the feature, but which do? SO has this question for SQL Server, but it seems more appropriate here.
PostgreSQL does not currently have it. But you are right, with MVCC it should theoretically be possible. In fact, the old university Postgres had an equivalent feature called time travel, but it was later removed because it caused too much overhead and the practical use was limited. While it would probably be possible to resurrect it, since then there have been many optimizations to the MVCC setup that would make it much harder.
The same functionality of Flashback Query can be achieved in SQL server by using
database snapshots. The catch? This feature is only available in the Enterprise edition. You can read more about it here.