If someone does this sincerely and with the intent of it being a gesture of taqwa (reverence towards Allah), love of Imam Husayn (A), respect for Imam Husayn  (A), respect for Islam, or something similar, it could be considered an act of worship due to their intention.

It would be similar to other acts of personal piety that vary from person to person, or culture to culture. For instance, many Shia wear black out of respect for Imam Husayn, but it is not a requirement. Rather, it is a gesture of respect, and a way of keeping the memory of Imam Husayn (A) alive in society. 

However, this is different from required acts of worship like salat which have a formal intention (niyyah) of worship. And it does not substitute for the required acts of worship such as salat.  

Some people use obscure stories such as "Zaynab hit her head on the camel litter or a pole" to justify self-flagellation. This is counterproductive and unnecessary. First, these stories are usually historically unsubstantiated. And, second, it is unnecessary, since we are speaking about acts that are personal and optional, not religiously required. 

Allah weighs actions according to intentions and what is in our hearts, and knows best what is accepted. We will see the reality of our deeds in the next world.