does it have to Phuket? You could try Koh Samui in August. Have been a few times and the weather is great. Yes- there are some showers but these tended to be early evening.

We were in Phuket this August. We knew it was the rainy season but hubby insisted on going to see what it was like. He assured me it would be showers but there would be lots of sunshine as well. We combined it with Samui and Bangkok.
As we descended into Phuket airport the areas around were flooded and it was pouring with rain. There was about 2 inches of rain as we walked across the tarmac at the airport. We found out it had been raining for 3 days and 2 nights. You can imagine how we felt because we had just left the sunny island of Samui.
However we were very lucky. We woke up the next day and it was brilliant sunshine. During the 6 days we were there we had just half a day rain. But it was raining again when we left.
Although we had a good time we would think twice before going to Phuket again in August.
Like Fiona says try Samui. We had 7 days of glorious sunshine.