I soloed Vaporeon!
After multiple failed attempts in the past I finally got over the hump today! My first attempt I led with Raikou and Zapdos and attempted to finish with my trio of exeggutors. Vaporeon had hydro pump and I came up just short. I tried dodging multiple hydro pumps and repeatedly missed the dodge (Hydro Pump comes super fast and the only times I can consistently dodge it is when I'm gym battling and attempting the dodge-all strategy). I timed out and probably needed about 10 seconds more.
However the second time, I switched up the order of my team (picture below) and went to work, intent on dodging at least 1 hydro pump. Raikou tanked the first hydro pump, but after just a little bit of overdodging, I dodged the second one. It allowed me to get off 2-3 more Wild Charges and the rest was history.
Raikou was the clear mvp as he took nearly a third of vaporeon's health. If you don't have one yet, I highly recommend powering one up. You won't regret it!

Answers
Awesome! Could you please give complete stats on your Raikou, including H/A/D ivs, CP (2870), HP, Level and Move Set.
Also, what do you think would be the effect of using a second good quality Raikou rather than a Zapdos. (I have better quality Raikous than Zapdos, so I would probably choose to power up two Raikous rather than one Raikou and one Zapdos.)
The raikou is a 100% level 30 2870 cp with TS/WC. My previous attempts came before I had Raikou, but I still had Zapdos (14H/15A/14D level 30 TS/TB). I failed on multiple occasions with a similar team, but I replaced the Raikou with a 93% TS/TB level 33.5 Jolteon. Since then, I've powered up the lower 2 exeggutors a couple levels a piece and tm'ed my zapdos (it had zap cannon but I wasn't very happy with it in general). The next problem was I just couldn't find a Vaporeon raid!
But to answer your question, I think the Raikou outperforms the Zapdos so 2 Raikou would presumably be better. Plus, I uploaded my pokemon into pokebattler.com and that site rates Raikou as my best vaporeon counter overall, and my anecdotal evidence agrees with the simulation!
Great work! I've tried two times this weekend and took down Aqua Tail but unexpectedly missed out on Hydro Pump (three tries, a sliver of red left). Hopefully Raikou will come here next week and then one of my Bullet Seed Exeggutors will be replaced.
Around level 30 lag and that sort of stuff plays a major role for beating Vaporeon and I highly recommend restarting the app before trying.