Well I suppose its already happening, if I understand correctly. Location data, search/browsing history, social connections/friends, all of this stuff that can be extracted by companies without it even seeming like exploitation. An alternative mine for value, instead of labor?
"Well its not like I'm working to generate that data."
That might be the crux. Data generation doesn't seem to require work, at least in the conventional sense. It just happens. All you need to do is be, provided you are accompanied/surveyed by the proper data recording apparatuses.
Yanis Varoufakis suggests the "universal basic dividend" which begins to think in terms of an economy that extracts value from data instead of just labor. This UBD entails Google would have to send out dividends as compensation for the data they use. This is likely to be meager stuff to start, but he seems to have interesting plans about it.
Also, the more data is collected by and incorporated into any algorithmic infrastructure, the better that infrastructure will get at collecting and incorporating data. At least to some extent, confined primarily by power costs/constraints for servers?
In terms of how class divisions would work, it seems like our current orientation will bleed over at least for a while, but I'm not sure if the class system will undergo such a shift as the economic system - really not sure here. That said, some speculation won't hurt.
Perhaps there will emerge ways in which one can generate more data than the next person. Perhaps there will be products that can increase your data capital (such as that monitoring device that sends you money for continuously giving it input/feedback as to what programming you are watching, what your watching schedules are like, etc.). Such things may very well become a trend.
This data economy may become more and more saturated with data that the dividual citizen will become so algorithmically knowable and predictable that they might as well not have a free will, in the conventional sense. This may sound dreadful - but I'm not so sure.
For instance, provided the database is accessible to all, which may be a major crux, this can allow anyone to monitor anyone. How privacy will figure into it, I'm not sure,
Perhaps the class division will be a privacy division, privacy being a luxury that only some can afford, seeing as traditional labor will likely become increasingly precarious and automated, data generation may be something of a dependable income. Not sure how currency as we know it will figure in, but perhaps it won't be too different from now.