Americans in Singapore - how to invest

If you are resident in Singapore, you can just open a brokerage account with any local bank and start investing.

First, you should open a bank account in Singapore. Either local or foreign bank is fine.  Then use that to fund your investments, presumably equities, in Singapore.

Yes the USA tax vultures have decided to hold the entire planet responsible for their tax collection efforts. You will now find it impossible to open almost any type of account w/ USA credentials in any country that values client privacy. The agreement that was savaged upon any countries that need USA relations or protections(pretty much everyone), is called FATCA. I would assert that the acronym was intentionally set one "T" short! Although the implication for USA IRS officials and everyone else is in opposition.
It is necessary to consult an investment advisor and maybe an attorney(In both the USA & SG) not random responses from an online forum. Depending on the type of investment; you could find yourself in serious jeopardy from the USA government if you fail to account for all that you might be susceptible to. There are USA based businesses that operate in SG and if you are talking about going into business there maybe someone willing to give you some friendly advice or recommend some services that could help you…Just an idea.

FATCA forces foreign businesses to report any earnings by an American citizen back to the IRS. Not suprisingly America does not reciprocate, it is a one way deal.

Sadly I am not surprised but was unaware of that.I was only aware of the banking issue. Funny under George W. Bush the liberals use international anti-US sentiment to shape political and even socio-political discourse. Now it seems the liberals are financially bullying the world with impunity. They are blood suckers that live to fund heaps of useless federal programs.
My former girlfriend was stationed at a military supply base in USA but she was RCAF(Canadian). She was filing legitimate tax returns w/ Canada and US tax returns showing no income in USA as she was a "resident".  The USA income form allowed her to claim an earned income credit!! She got money for free because she had a dependent child!!