To what I read from the papers, you will need to buy AND use the test kit under the supervision of the clinic's doctor. This means that it is not an anonymous test, as positive results will be reported to MOH by obligation.
At present, there is no Over The Counter (OTC) product for "test @ home".
Singapore's policy regarding OTC HIV test kits would be to let the US FDA domestically approve it first, before even considering it locally.
In the US, there is currently no OTC HIV Test kits available. However, there is the option to purchase a Home Access Kit and to send in the blood samples to a lab and access your results through a telephone call. More information available from
http://www.homeaccess.com/. Home Access is available in the US only.
OraSure in the US are FDA approved for Point Of Care (POC) use, much similar to what AfA is doing at their Anonymous Testing Centre.