My page numbers will be coming from the edition published in 2011 in the UK, so they might be a little different. I will try to give an approximation of where they are in each chapter.
One of the biggest literary devices in the entirety of the Hunger Games series, which is showcased in Chapter 9, is the symbolism of fire. Katniss is the "girl on fire" and the flames follow her through the series, starting at the parade of the Tributes. Saying that you are "on fire" means that you are on a roll, experiencing success, and doing very well; Katniss has started this roll by appearing in the Capitol and catching the crowd's attention. The fire also symbolizes that Katniss is a hot topic in the Capitol due to her brave volunteering. "The slightest movement gives the impression I am engulfed in tongues of fire." (pg. 146, halfway through chapter 9, after Cinna gives Katniss her dress) It also symbolizes her temper, her heat: "'Guess they liked your temper,' he [Haymitch] says. 'They've got a show to put on. They need some players with some heat.'" (pg. 132, two-thirds of the way through ch. 8, after the Tribute scores are revealed and Katniss receives an 11 out of 12).
There are also flashbacks, which are simply a way to tell the story out of order and put emphasis on specific events. One such example is when Katniss is recalling how she met and became friends with Gale about two-thirds of the way through chapter 8 (starts on pg. 133). I am not going to give a direct quotation for this because there is no single quote that would be helpful in showing the importance of the moment. Instead, I will give a general overview: they met in the woods while he was trapping and she was shooting, and they slowly grew to trust each other and exchange their knowledge; throughout that time, they became close friends and confidants. This is something Katniss misses in the Capitol, when she is alone with people she is not as familiar with and she needs comfort.
There is also the tone of these chapters. Katniss' dryness, her "sullen and hostile" attitude (pg. 141, beginning of Haymitch's tutoring at the beginning of chapter 9), is how she frequently responds to the events around her.
These are but a few of the literary devices; there are many more, such as characterization, first person point of view, setting, etc.