If you are looking at getting a cheap life jacket in Singapore, you can purchase one for around S$15 at the Army Market located at Beach Road. The following is a picture of the life jacket that I bought from one of the shops found there, as well as the location map of the place. A word of caution: before you start using it in the open sea, be sure to test it out thoroughly in shallow water or a pool.
Location Map of Army Market at Beach Road
View Army Market At Beach Road in a larger map