See README below.

README

INSTALLATION

Copy jenkins-slave.init to /etc/init.d/jenkins-slave and copy jenkins-slave to /etc/sysconfig/jenkins-slave.

cp jenkins-slave.init /etc/init.d/jenkins-slave
cp jenkins-slave /etc/sysconfig/jenkins-slave
chkconfig jenkins-slave on
service jenkins-slave start

Change the values of /etc/sysconfig/jenkins-slave to match your environment needs. 
It's critical that JENKINS_URL and JENKINS_NODENAME are set.

The node name variable must match a node that you've already defined in your Jenkins nodes.

jenkins-slave

JENKINS_WORKDIR="/opt/jenkins-slave"
JENKINS_USER="jenkins-slave"
JENKINS_URL="http://127.0.0.1:8080"
JENKINS_NODENAME="slave_name"
JENKINS_SECRET="SECRET"

jenkins-slave.init

#!/bin/bash

# chkconfig: - 85 15
# description: Init script for jenkins-slave

# Source function library.
. /etc/rc.d/init.d/functions

[ -f /etc/sysconfig/jenkins-slave ] && . /etc/sysconfig/jenkins-slave

[ -n "${JENKINS_URL}" ] || exit 0
[ -n "${JENKINS_WORKDIR}" ] || exit 0
[ -n "${JENKINS_USER}" ] || exit 0
[ -n "${JENKINS_NODENAME}" ] || exit 0
[ -n "${JENKINS_SECRET}" ] || exit 0
[ -x /usr/bin/java ] || exit 0

create_user()
{
    awk -F":" '{ print $1 }' /etc/passwd | grep -x ${JENKINS_USER} > /dev/null
    if [ $? -eq 1 ]; then
        useradd ${JENKINS_USER} -d ${JENKINS_WORKDIR} -s /bin/false
    fi
}

create_dir()
{
    if [ ! -d ${JENKINS_WORKDIR} ];
    then
        mkdir -p ${JENKINS_WORKDIR}
    fi
}

create_logdir()
{
    if [ ! -d /var/log/jenkins-slave ];
    then
        mkdir -p /var/log/jenkins-slave
        chown -R ${JENKINS_USER}:${JENKINS_USER} /var/log/jenkins-slave
    fi
}

download_jar()
{
    curl -s -o ${JENKINS_WORKDIR}/slave.jar ${JENKINS_URL}/jnlpJars/slave.jar || exit 0
    chown -R ${JENKINS_USER}:${JENKINS_USER} ${JENKINS_WORKDIR}
}

start()
{
    create_user
    create_dir
    create_logdir
    cd ${JENKINS_WORKDIR}
    [ -f slave.jar ] || download_jar
    echo -e $"Starting Jenkins BuildSlave..."
    su - ${JENKINS_USER} sh -s /bin/bash -c "\
            /usr/bin/java -jar ${JENKINS_WORKDIR}/slave.jar \
            -jnlpUrl ${JENKINS_URL}/computer/${JENKINS_NODENAME}/slave-agent.jnlp \
            -secret ${JENKINS_SECRET} \
            >/var/log/jenkins-slave/jenkins-slave.log 2>&1 &"
}

stop()
{
    echo -e $"Shutting down Jenkins BuildSlave..."
    pkill -f 'java.*slave.jar'
}

# See how we were called.
case "$1" in
    start)
        start
        ;;
    stop)
        stop
        ;;
    restart|reload)
        stop
        start
        ;;
    status)
        status java
        ;;
    *)
        echo $"Usage: $0 {start|stop|restart|reload}"
        exit 1
esac

exit 0

Grant execute permission to the init script
sudo chmod +x /etc/init.d/jenkins-slave

Should it not be:
sudo chmod +x /etc/init.d/jenkins-slave/jenkins-slave.init
?

this needed for service to auto start
sudo systemctl enable jenkins-slave.service