MySQL rapid Data Replication from multiple Databases
Some might say depends how big the databases are; I think regardless of the size, accessing the databases directly instead of having a "local" mySQL database to query would be best, for the following reasons:


No need for disk/memory/maintenance of the mySQL database
If the updates to the various databases happen every few seconds, and the users may only use the web page every few minutes/hours/days, you are executing a lot of queries that are not needed most of the time, which in turn places additional load on the six databases. In other words, I think the client doesn't realize the impact of having a replication scheme.  Even if just a few tables from each database is involved, the synchronization code running every few seconds would be much worse than occasional specific queries (occasional being something running every few minutes/hours).
The code to replicate data from 6 separate databases would be quite complex to do correctly.