There are 25 flights connecting Phuket and Singapore every week, with the journey taking 8 hrs 40 mins on average.
Or, if you're fairly flexible on dates, try to get a last minute-deal by regularly checking the Netflights website.
In Singapore, Singapore Changi International Airport (SIN) is usually the cheapest airport to fly to, but there are one airports to choose from. Not sure who to fly with? Malaysia Airlines & China Eastern Airlines are the most popular airlines available from Phuket.
But if you can't find one which is right for you, try looking at flights to other cities in Singapore to check out some other options.