There are at least two ways in which Lincoln's childhood experiences are said to have impacted his views on slavery.
First, Lincoln's family belonged to a church known as the Separate Baptist church. This church was opposed to slavery. Lincoln may have absorbed some of his attitude towards slavery from this.
Second, Lincoln's family was forced to leave Kentucky and go to Indiana when Lincoln was about 7 years old. This move was caused mostly by conflicts over the title to the land that Lincoln's father had believed he owned. However, Lincoln himself said that part of the reason for the move was opposition to slavery.
Beyond that, we know little about how Lincoln's childhood might have affected his attitudes on the issue of slavery.