Will have to write an import utility from BDE to MySQL.
BDE is a tool to connect to and operate on database tables, not database in itself. So you have to think in two separate tasks.
1) Moving Paradox tables (and queries, etc. if exist) to MySQL database
2) Using SQL connection, instead of BDE.
First one is easy. But if you are not familiar with relational database, the second task may need some study.