The slavery that Paul speaks of is not a forced slavery but rather a slavery of love. It is freely chosen and it is the fulfillment of love. If you think about what a married couple vows to one another when they make a vow to love, it is a vow to serve one another every day for the rest of their lives.
And what is love? It is serving the other. It is seeking the good of the other. Jesus has made himself a slave to us and he serves us. In return, we make ourselves a slave to him by serving him, doing his will, seeking his good. It will not be difficult for us to do so if we keep in mind that Jesus himself took the form of a slave and he came to serve us even to the point of going to the Cross. Jesus is the sign to us. He is the One Who came into this world and took the form of a slave. He was obedient even unto death on a cross. He is the One who teaches us what it is to love. He is the sign for us, the sign of what it is that each one of us is called to, the sign to be able to reject sin and embrace our own dignities, to love as God created us to love. And what is it to love? It is to be brought into the obedience of faith, to live what we profess, to be voluntary slaves of love of Jesus Christ.