Look at the error message:
The INSERT statement conflicted with the FOREIGN KEY constraint FK_Leagues_LeagueTypes. The conflict occurred in database KADB, Table dbo.LeagueTypes, Column Id.
The table has a Foreign key relationship with a different table, and you are trying to insert a value to the ID column which does not (or more likely cannot) exist in that table.
Check your table definitions, and make sure you haven't got the foreign keys the wrong way round or similar: If you can't work it out, post the actual SQL table definitions and show the actual data that currently exists, plus the INSERT statement you are using that fails.