Is it safe to flush newspaper down the toilet?
No, that would not be safe.  If you want to use something other than regular tissue (like paper towels), you would need to dispose of it in the wastebasket.  

Toilet paper is made to fall apart quickly when it gets wet and doesn't contain any chemicals that would harm a septic system or a city's sewer treatment.  Newspaper isn't the strongest paper, but it doesn't fall apart as easily and the ink and paper itself might contain harmful chemicals.