The best method would be to take the code the sqlite3 db dump would do, excluding schema parts.
Example pseudo code:
SELECT 'INSERT INTO ' || tableName || ' VALUES( ' ||
{for each value} ' quote(' || value || ')' (+ commas until final)
|| ')' FROM 'tableName' ORDER BY rowid DESC
See: src/shell.c:838
(for sqlite-3.5.9) for actual code
You might even just take that shell and comment out the schema parts and use that.