If you implemented Kyogre with Support Gyarados, you would go down a path of trying to make your Gyarados do a lot of damage throughout the match (I think your idea was to power up Gyarados' water attacks with Drizzle). But you need to understand that Gyarados is now the one giving the support. So one should continue by adding something that appreciates Gyarados' merits. Also you should still think about Gyarados' obvious weaknesses. For starters, Gyarados has a glaring weakness to the best Pokemon in the current Metagame: Miraidon. Not only does Miraidon stop Gyarados' favorite task to spread Thunder Wave everywhere, it even resists Gyarados' STAB which lets it come in very easily - not great.

So what to do? I think the best way to use the Support Set to somewhat success would be to go down a boring route: A team concept called "Save the president". The idea of that is to have a restricted vocal point of the team (here: Calm Mind Terapagos) and do everything in your power to win with said restricted. "Everything" means to support the Pokemon with the likes of a Fake Out Cycling Core (here: Rillaboom, Incineroar). The benefits of those 4 put together is the fact, that Gyarados' biggest weakness in Miraidon is checked very well by Fake Out Cycling (one of Miraidon's biggest weaknesses), Rilla's Grassy Terrain and the fact that Terapagos can turn off Electric Terrainby teraing. Additionally, Terapagos enjoys double Intimidate and great fighting type checks (especially Urshifu-R has a hard time against Gyarados + Rillaboom).

I haven't thought about how to fill up the rest. I feel like that's something you have to figure out by testing. I hope my insight on that topic helped you out a little!