The red cross flea market (at least on Penang Lane) I think is a good option especially when it comes to buying clothes or accessorize. Last time I went there I found this gorgeous black Zara jumpsuit and lots of designer shoes and cute vintage jewelry. The only downside is that it's only open on Wednesdays :(

http://www.redcross.org.sg/articles/shopredcross-low-cost-great-cause


For shopping furniture, deco or anything to do with interiors, Junkie's Corner is the best. They have a lot of crap to be honest, but I found a Marilyn Monroe poster and a gorgeous vintage crocheted bag that looks like it's taken straight from the Dolce& Gabbana fall 2012 collection.


Of course I have to mention the classic Salvation Army fleamarkets, because whatever country or place they are in, I never fail to feel serendipity when I enter their store. They might not have designer labels or anything special but there's always something for everyone.

http://sarsifts.wordpress.com/shops/

Here's some more that I didn't mention yet:
http://www.expatliving.sg/living_in_sg/settling_in/5-of-our-favourite-flea-markets-in-Singapore-26503.ece