Some parents do become jealous of their children if the child excels or exceeds them in a skill. Some parents become jealous when their children get all of the attention. Many times new dads will feel jealous of the time mom spends doting on the baby for example.
Most parents are pretty well-balanced though and I don't think jealousy is as big of a problem with parent/child as it tends to be among younger siblings. Of course jealousy in general is usually an indicator of someone who needs to be more self-focused in a positive way - instead of envying what someone else has, focus on what you can do and do well.