Firstly, there is no flight from Beijing and Shijiazhuang since they are close to each other.

However, I'm afraid that you could not catch up the last train departing from Beijing West Railway Station to Shijiazhuang at 22:45. So, it is suggested that you stay one night in Beijing.

Well, when you arrive at Beijing Airport, please take the shuttle bus Line 7 to Beijing West Railway Station directly. Here, you could find a hotel for one night easily. On the next morning, you could take the first bullet train at 06:21 to arrive in Shijizhuang in 2 hours.