喉がかわいてきた

The phrase combines '喉' (nodo, throat), the particle 'が' (ga, subject marker), 'かわく' (kawaku, to become dry) in its te-form 'かわいて' (kawaite), and 'くる' (kuru, to come) in its past tense 'きた' (kita). The combination of the te-form of a verb with 'くる' often indicates a change of state that has been happening and is now somewhat complete or has reached a certain point. In this context, 'かわいてきた' suggests a gradual process of becoming dry (thirsty) that has 'come' to the speaker. '喉がかわく' is a common way to express thirst, literally 'the throat becomes dry'. The addition of 'きた' adds the nuance of 'starting to feel' or 'has become' thirsty, emphasizing the onset or progression of the feeling.