Colin Kaepernick did not randomly choose the time of his protest. 

"'I am not going to stand up to show pride in a flag for a country that oppresses black people and people of color,' Kaepernick told NFL Media in an exclusive interview after the game." (full story here: http://www.nfl.com/news/story/0ap3000000691077/article/colin-kaepernick-explains-why-he-sat-during-national-anthem)

He was very deliberate in choosing the flag and the anthem to protest.