How to change Jenkins' port to 80?
Assuming you are okay with moving your Jenkins(and settings) to a docker environment, you can do the following. This would give you the advantage to change ports(and manage jenkins) with greater ease in the future without ever having to touch IP tables or load balancers.

Host your Jenkins on a docker container and map the port 80 on your docker host daemon to 8080 on the container.

You can find the latest jenkins docker image here - https://hub.docker.com/_/jenkins 

Install docker daemon and download the image using
docker pull jenkins

You can use docker run command to start jenkins along with the -p argument to supply port values.

For instance, you are hosting your docker daemon on 10.10.169.69, then you use this to start Jenkins
docker run -t container_tag -p 80:8080 image_name

And then to browse jenkins, use http://10.10.169.69:80/