Compared with, say minimum wage increases, how inflationary is progressive taxation?
This is almost a link only answer, but you are asking for peer reviewed sources in the comments.
Brian Romanchuk's statement that taxes are anti-inflationary also appears. (Attributed to 'conventional macro'.)
Conventional macroeconomics classifies an increase in the rate of income taxation as an anti-inflation device because it reduces aggregate demand. However, an income tax hike may also constrict aggregate supply, making the effect on the price level ambiguous on purely theoretical grounds. This phenomena is investigated in the context of the conventional Hicks-Hansen IS-LM model, and a sufficient condition for an income tax hike to reduce the equilibrium price level is found. It is argued that this condition is very likely to be satisfied by the U.S. economy.
Taxation is deflationary. It's fiscal tightening. It reduces aggregate demand.
(You didn't mention government spending in the question, so I've assumed it's flat).
Inflation is an increasing amount of money chasing the same amount of goods (or variants of same).
Taxation reduces the amount of money in the economy. So there's less money chasing the same amount of goods. Hence it's deflationary.
As to the extent to which progressive taxation specifically, is more or less deflationary than flat or regressive taxation: if we accept the observation that marginal propensity to consume decreases with income, then progressive taxation is less deflationary than flat or regressive taxation.
If, instead of assuming government spending is flat, we assume that the government's net fiscal position is flat, i.e. spending changes to match tax revenue, then progressive taxation is likely to be inflationary relative to flat or regressive taxation, as the average propensity to consume of people on lower incomes tends to be higher than that of people on higher incomes. Whether the overall net effect of taxation is inflationary or deflationary, will depend on the exact nature of the government spending, and where the economy is in the cycle.