I have some equipment that uses 8.5 amps and 1050 watts on a 110v. Any idea what the amperage would be on 208 three phase?
A 208 volt 3 phase supply has line voltages of 208 volts and a phase voltage (line to neutral) of 120 volts as per this diagram: -
So, if your equipment can run from line to neutral and is just a passive load like a heater then the watts will tend to increase a little bit more as its supply voltage increases from 110 V to 120 V.
If the equipment is more sophisticated then it may be slightly more power efficient or slightly less power efficient at 120 V compared to 110 volt but this cannot be determined by the detail in the question.
Even if it were known what the equipment precisely is, there may be no data available that shows what power consumption it will have at 120 volts compared to 110 volts.