Badge or Dragonites.

I mean, I think it's much easier to do this with Trapinch than with dratinis...or even find bagons wild

The question is, with 3 maxed Dragonites, why would you want more? Go for the badge for what it's worth.

If the question is "will I get enough Dragons to get a Gold Badge to help catch Rayquaza before Rayquaza goes away?", I don't think you will, so in that case I wouldn't rush it. Dragons are easier to get nowadays with gen 3 additions, meaning you can find them in a lot more biomes and eggs somewhat more readily.

One guy here caught over 200 hundred dratinis, you must have been in the wrong place

Just to be first person to use https://pokeassistant.com/main/pidgeyspam to see how many Dratinis you can mass evolve into Dragonairs?

Evolve and max Dragonites

I know someone who did some dratini grinding to get the gold badge, but it was only a dozen or so evolves.

If you’re goal is the gold badge while RayQ is still around, maybe you should hold off on the evolving until you line up enough to put you over the top. 550 candies won’t get you even half way there.