Inserting into multiple tables simultanteously (HEIDISQL)
The overhead and complication of spinning off two threads to run the queries simultaneously are almost always more costly than doing them sequentially.

Copying an entire table over is normally a rare task.  As such, the performance is often not a big deal.  Are you doing this as part of the normal flow?  If so, let's look at it in more detail to see if there is a better way to achieve the ultimate goal.

Don't use TINYTEXT.  VARCHAR(255) (or some smaller number) is virtually equivalent, yet more efficient in some situations.

Redundancy:

PRIMARY KEY (`componentno`, `flatpackid`),
INDEX `componentno` (`componentno`),    -- DROP, since the PK handles it.