Prattled-(Verb):to talk for very long about something that is not important or interesting.

http://www.merriam-webster.com/dictionary/prattled?show=0&t=1382843065

As she prattled to Alfred about bicycling in Prospect Park or rubbing bicarbonate of soda on the sunburn she’d gotten on a trip to Coney Island with her girlfriends, it would cross my mind that I knew the time and place of the death that awaited her.

I understand the author is saying that she was telling Alfred information that was not important or interesting to hear.