How many countries have flags that consist of both red and white and only those two colours?

Either 16 or 18, depending on whether the maroon-like colour murrey is classified as a type of red. Latvia and Qatar's flags are technically white and murrey. The other 16 countries are:

Austria, Bahrain, Canada, Denmark, Georgia, Indonesia, Japan, Malta, Monaco, Peru, Poland, Singapore, Switzerland, Tonga, Tunisia and Turkey.

Although not countries in their own right, these flags are also red and white:
Gibraltar, Greenland and Hong Kong.

https://worldpopulationreview.com/country-rankings/countries-with-red-and-white-flags

A quibble regarding Malta is that the George Cross awarded to the country appears in other colours (black and grey) on the white half. See https://en.wikipedia.org/wiki/Flag_of_Malta