How do I get back on the Valkyrie on Battlefield 4 during the south china sea mission?

Use and hold your boost key to gain extra acceleration.  It's shift on PC, not sure about consoles. It's likely the same as what you use for sprint while running around with your soldier on foot.

I also had this problem -- getting back to the Valkyrie.  I must have been driving the speedboat behind a battleship and the Valkyrie carrier for maybe about 45 minutes.  Finally I gave up.

A plane did fly over.  I have been playing this game on the Xbox 360.  At one point I was able to drive up alongside of the ship, either side, but there is no way to re-connect with the Valkyrie ship.  I will try to start over as others have suggested.