Is there a method to date rock paintings with red paint (magnetite) though paelomagnetic techniques, such as paleointensity? They are painted on sandstone (quartz-arenite composition).
Yes, there is a method that may be tried, based on the assumption that paintings acquire a "pictorial remanent magnetization", which can be compared to local reference curves of paleosecular variation of the geomagnetic field.
As a starting point, you may have a look to the following paper, published on 1997 and available on Research Gate: https://www.researchgate.net/publication/248216054_Pictorial_remanent_magnetization_as_an_indicator_of_secular_variation_of_the_Earth's_magnetic_field
Article Pictorial remanent magnetization as an indicator of secular ...