When trying to export to MySQL after adding additional entries I get a foreign key violation because JabRef tries to DROP TABLE IF EXISTS entry_types. As entries already has rows this causes the violation. By the way rewriting the whole database each time does not make sense especially for larger tables.
Simple way to fix it but not recommended:
First check if tables already exist. If so and you want to rewrite the whole database you have to drop the tables in the correct order first those referencing other and then the referenced ones. Means entry_group first, entries second and then all the others can follow. Simple and not really a good idea especially if several people want to share and update the database.
Do a real synchronization between the local bibtex file and the database or let the user choose which storage should be the leading one. If you need help on the database logic feel free to contact me as I am a database expert.