Translation:We ran to each other
Kukimbilia is the prepositional form* of kukimbia. Since the verb ends with a double vowel, one has to insert -li- (or -le-) before the final -a. (and just -i- or -e- in verbs ending with a single vowel).
Googling for 'kimbilia', I found this example:
Wakati wa vita, Wanyrwanda wengi walikimbilia Tanzania
During the war, many Rwandans ran (fled) to Tanzania
- According to Wikipedia 'prepositional' is actually a misnomer: it is actually the 'applicative voice': https://en.wikipedia.org/wiki/Applicative_voice#Swahili