DXY measures the US dollar against every other currency. So if the US dollar in isolation had a bunch of inflation (e.g. because the US government printed a ton of money), then that would be reflected in DXY.

But if every major currency printed a ton of money at the same time, then DXY would not change because it’s only relative to other currencies.

So it doesn’t calculate inflation directly, but it’s generally correlated with it.