Welcome to the Ranch.
When database needs to synchronize data, it usually done through replication using the database provided tools. This will mean the primary database is the one user insert/update/retrieve data and let the database do the replicating to the secondary database in its own time frame. I'm sure this time frame can be set long or short.
when i insert data in master database table1(name, boolean), it should be automatic insert into slave database table1 (name, only when boolean is true).
Given your requirement, if replication is used, the slave database will have data that are boolean=false too. I'm no DBA maybe it can choose what data to replicate. So do check with your DBA first.
If nothing seems to work, then you would have to manually insert into both databases.