Yes, self-flagellation has occured in many instances in the Western Catholic tradition. Many great saints have been known to wear constantly-itching hairshirts and whipping themselves, or "using the discipline" as they put it: St. Catherine of Siena, St. Thomas More, St. Ignatius Loyola, St. Josemaria Escriva. Other forms of mortification have been practised as well: pope St. John Paul II was known for sleeping on the floor, then making his bed in the morning to make it look as if he had slept in the bed.
The wearing of chains is a symbol of being a slave of Jesus and Mary, often associated with St. Louis-Marie de Montfort, and these are more of a symbol than true mortification.
Extreme forms of mortification (hairshirt, cilice, self-flagellation) should only be done under guidance of a spiritual director. Actually, doing these things without the approval of a spritiual director might even be sinful. In the 1300's, the Catholic Church condemned the Flagellant movement as heresy because they were totally out of control.
So these mortifications are good spiritual practices ... but only for those who have that particular calling. Otherwise, for those without this calling, it will do more harm than good. As far as I know, extreme mortification is extremely rare in the Catholic Church today. And the few who practise it will go to great lengths to conceal and hide it, to avoid the sin of pride. And even then, it is very regulated: we talking about whipping your back while saying the Our Father, once a week. Or wearing a cilice/hairshirt for two hours at a time.
There are plenty of less extreme forms of mortification we all can do. And oftentimes, being kind and forgiving towards your fellow man can be a lot more difficult than simply lashing your own back for a minute.