First, let me clarify that US taxes, in general, do not exempt staff travel. Some do, but most do not apply to free tickets and since most US employees are not assessed service charges on their own airline's domestic flights, taxes do not apply. You would collect taxes on reduced fare (e.g., ZED or ID90) tickets because you're collecting a fare amount. There are a few international taxes that don't apply to free travel, travel specifically by airline employees, travel by airline employees on business, etc.
There are three taxes that apply ex SIN, they are the Passenger Service Charge (SG1), the Passenger Security Service Charge (OO), and the Aviation Levy (OP). The rules and amount applicable vary for each.
SG1 = SGD13.90 pretty much, applies to every traveler type, except airline crew on duty/positioning
OO = SGD8.00, same application
OP = ranges from SGD2.20 to SGD6.10 depending on the transporting airline and also applies to pretty much everyone but crew.
On a SIN-HKG IDZM3R2, for example, the total tax would be SGD28. The same amount would apply to SIN-FRA IDZM8R2.
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