You wont have any difficulty finding formula and baby food unless you are after a particular brand. The "Big C" shopping centre has the best variety, but you will need transport to get there from the beach areas. The Ocean PLaza in Patong will have a more limited selection , but if you and the baby aren't too fussy, you should find it adequete.
The only thing that we ended up taking from home was disposable "Huggies" nappies, as everything we bought in Phuket would leak. We always would fill a case with nappies and then use this for our shopping space.

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