Not always, and no.

New money is created all the time, and most of it not even by government spending, but through businesses taking loans.

When governments spend too much in competitive markets, i.e. on resources that aren't there yet, then yes it drives up prices. Just running a deficit does increase the money supply, which still only causes inflation in some cases.

The classic inflation from the economy working a little too well is not a flat tax, since both wages and prices are growing. Savings on the other hand (except stocks), lose their value. Classic inflation erodes the savings of the rich, and erodes the debts of the poor.

And even then, the central bank can always increase the cost of businesses lending to slow things down. That has other downsides, but the point is:

1. Government deficits don't always lead to inflation
2. When they do, a bit of inflation is not a bad thing, since wages grow too

But yes, tax the rich. Can't argue with that