For all Platinum has to offer, you've got yourself a decent team without knowing the movesets.
You could change Kadabra to Starmie, then you have a psychic type and also a water type. If you want another water type you can change to Floatzel.
I recommend Garchomp as your sixth Pokemon. It's both ground and dragon type and it is very strong! :D
If he can't trade in-game, then he could swap for Starmie (equally as versatile, can learn better attacks like Ice Beam, Surf, Thunderbolt among others. It's super fast and has superior Special Attack.) I also second the Garchomp nomination, it has amazing Attack power, good Speed and good enough defenses to survive attacks.
Optional: Get a Pokemon that can take a ton of hits, even something like Noctowl, and teach it Toxic. Toxic inflicts stronger and stronger damage each turn the poisoned Pokemon is out. Since the average Trainers and your rival don't typically heal their Pokemon, this strategy is an easy way through some tough battles. Speaking of tough battles, the Gym Leaders and the upcoming Elite Four heal their Pokemon almost everytime they reach red health.
TLDR: Get Starmie (you need a Water Stone, but since you found a Shiny Stone, a Water would be no trouble.) and Garchomp (Rare to find Gibles, but they're in Wayward Cave, conveniently located under Cycling Road near Eterna. You need Flash and some high-quality balls like Ultra Balls.) And if worse comes to worse, just run with the team you have. It has enough type diversity to get through the game, but they of course need training.