Taman Tun Dr Ismail has a few 2nd hand furniture stores! There is indeed one near Devi's Corner but I feel that one is not stocked very well.
There is a good one behind the row of bars and pubs near Villa Flora. It's called Second Charm (http://charm2nd.blogspot.com/). There is two levels... the ground floor has the usual hand-me-down knick-knacks -- fashion, old tableware, vinyl LPs, etc, and a few pieces of furniture... the woman jaga-ing the counter told the 'furniture' section was upstairs - to my utter excitement! It was a whole store room of modernist pieces, vintage dusty stuff, old headboards, cupboards, seating. I spotted a stack of white moulded Panton chairs - I assume they are fakes... but still! What interesting finds in a completely nondescript, sleepy shoplot! I could tell the owner is quite passionate about vintage furniture and the restoration process, judging from the blogspot...
The Rockwood Enterprise (http://rockwood.en.ecplaza.net/) also in Taman Tun specialises in Teak furniture. I spotted some interesting pieces at their storage upstairs... 1960s Javanese mirrors crafted in playful shapes (mini headboards with beautiful stained glass details, a ship, a motorcar...). The place is managed by the rather amiable Mr. Rock... besides vintage, they can have custom orders... design your own and they will get their craftsmen in Indonesia to make it for you, shipped within a month.
Another charming spot for vintage furniture is The Curiousity Shop (http://thecuriousitygallery.blogspot.com/) located along Jalan Berangan, Kuala Lumpur, in a pre-war intermediate lot, surrounded by other quaint lots, new cafes/restaurants and the elegant Rogue Art gallery (http://www.rogueart.asia/).
There is another of such stores in Sungai Buloh somewhere, but I'm not certain where. I saw an exhibition using a lot of pieces from that shop - kopitiam furniture, bent wood chairs, 70s fixtures... anyone here know