In most jurisdictions property taxes are not progressive, they are flat relative to the value of your house.  That is to say you pay the exact same rate whether your home is worth $100,000 or $20,000,000.  The latter would pay more in absolute dollars but the rate stays the same, hence a flat tax.

One could make an argument that property taxes are regressive relative to income levels, though there is not a direct relation.  Generally speaking people earning, let's say, $50,000/year would pay a higher proportion of their income toward property taxes (either directly or buried in their rent) then a person earning $5,000,000 would.  The latter would pay more in absolute dollars but possibly less as a proportion of their income.

This is a bit of a tricky argument to make though since someone earning $5,000,000 could well live in a very economical 1-bedroom apartment or some such.