Yes, in the second book, Catching Fire, she does.
Spoiler alert:
After Gale is almost whipped to death, and comes to Katniss's house to be treated by her mother, Katniss kisses him before telling him that instead of running away, she has decided to stay with Gale and try to rebel against the capital. This does not mean that she had chosen Gale over Peeta, though.
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Peeta and Katniss.Catching Fire revolves around Katniss's fake pregnancy with Peeta's child and their marriage. There is small Katniss/Gale mentioned, such as Gale's quick kiss with Katniss, but the main pairing is Katniss/Peeta.
Gale loves Katniss. He admits that to her in Catching Fire when they kiss at the beginning of the book. He defintely wants to be more than friends, and so does Katniss at one point. SPOILER: She does end up choosing Peeta, because Gale become a bit of a jerk at the end of Mockingjay.
they are best friends, but then they start liking each other after the hunger games. she chooses gale over peeta in catching fire but then in mockingjay gales moves to district 2 and katniss and peeta get married and have kids
Katniss and Gale kiss three times. Twice in catching fire and once in mockingjay. Unlike her kisses with peeta katniss knows there were full of love. although she is not totally sure how she feels about the first one. Gale loves her, and she loves Gale but she knows the captiol expects her to be madly in love with Peeta.
Snares