From the full paper: "Although reading with children did not change over time, rates of engagement were surprisingly low, with only 2% of participants reading with children on the average day. Overall, 21% of our sample had a child under 9 years (the age by which most can read independently) with them during the diary day. So a large majority of those with young children did not read with them."

So of people with young children, it looks like the rate is about 9.5%.