I know that a USB 2.0 port can deliver 500 mA and USB 3.0 can deliver 900 mA.
Is this any different on a phone, because it is a smaller device? I was thinking maybe it would be a smaller amperage, like 100 or 200 mA?
"how much current does a phone USB port deliver?"
It only delivers anything when in USB-OTG mode. This isn't as well-known as normal USB. This article describes USB-OTG power in more detail.
The OTG spec calls for at least 8mA and allows negotiation for higher currents if the peripheral needs more power. OTG devices can provide up to 500mA, but in realistic terms, handheld portable electronics don't have 500mA to spare for external loads. 100mA is a commonly accepted realistic maximum.