Is it OK to contact conference chairs and volunteer to review (specific to Data Science Conferences)?
There seems to be an explicit question, why you have not been invited to review papers, and an implicit one, why you have not been invited as a PC chair.

Reviewing papers

As a PhD student you should have been given papers to review, but these papers will not be given to you by the PC chair but rather PC members who may delegate one or two papers to you. The most likely people to delegate paper reviews are your supervisor(s), you could ask them.

Becoming a PC member

Since you mentioned volunteering to be a reviewer, it seems you might have being a PC member more in mind. Typically, you can only be a PC member after obtaining your PhD. At this point, people who know you should suggest your name, such as your current supervisor(s), people you meet at a conference (this has happened with me) or your new colleagues (e.g., a PI) if you move on after your PhD.

For the specific question, if you know the general chair quite well, then I think it is okay to ask if you can help out as a PC (once you have your PhD). If your supervisors or other close collaborators are SPC, you can also ask them to suggest your name. But I suspect once you have your PhD you will be asked anyway. 

This is only based on personal experience, no-one can say for sure whether a given person will mind.