Firebird is a database to which you connect to - similarly to MySQL or PostgreSQL. So Firebird doesn't 'work with' SQLite - it's up to your program to connect to various databases and work with them accordingly.

So in my VB .Net application, I can create a connection to the Firebird database, then create another connection to a SQLite database and pull out records accordingly.

Creating a link between the two could be more problematic - reading both databases as one and pulling in tables into one query. It would be easier to import data from one system into the other.

Rather than problem X (what is the connection string), what is problem Y? (ie, what are you trying to achieve?)