There isn't the flexibility because trains don't come to Phuket for a start and there aren't many train services in Thailand anyway.
Train times Singapore - Kuala Lumpur - Hat Yai/Surat Thani are here
http://www.seat61.com/Malaysia.htm#Train%20times but it takes a life time on the train. You would have to get off at Hat Yai or Surat Thani and get a bus. You're talking about 8 hours to Phuket by bus from Hat Yai, 4 hours from Surat Thani.
Why not fly...or if you want to go by train so much get off at Sentral in Kuala Lumpur, get the Skybus to KUL LowCost terminal for 9 Ringgits and fly Air Asia direct to Phuket in 75 minutes?