There are two possibilities: the worst is that the welder uses both 110
and 220, the 110 coming from 1 leg and ground. This isn't approved, but
might be. In this case, wiring green and white to the 2 flat pins
would put 220 on the 110 circuit and fry it. You have my condolences.

The other possibility is that the welder only uses 220 and the green
wire is for (case) ground only. This is more likely and mis-wiring is
less likely to damage the welder (it would result in 110 being applied
to the welder's 220 input). Less likely, but still possible. It is
more dangerous, though, as 1 leg (110) would be applied to the case and
could give you a shock.

Did the welder come with a diagram of the internal wiring? You could
tell from that if the green wire was ground only or used as neutral for
a 110 circuit.

Bob