Call for help
In retrospect, it appeared that Kyle barking at the oak tree was a cry for help. And from one specific person. Kyle missed his old partner John and needed him. Through his act, he got exactly what he wanted. He was reunited with his true owner.
But Kyle missed more than just his friend. Ever since he moved in with the Smiths, he missed the hustle and bustle of the police force. The area surrounding the house was beautiful, but Kyle clearly needed more of a challenge. He creatively came up with a case to solve.