How can I publish an academic paper independent of work while working at a company?
If my research paper is completely unrelated and independent of anything I do at work (nor am I even in a research type position), what - if any - obligations do I have to my work place? Do I need to seek their approval before publishing a research paper?
  


You would have to read whatever NDA you signed, as this is specific to your situation. IANAL, but I think the most likely answer is there is no problem with this. You aren't allowed to divulge company secrets, but this is something you worked on independently (somewhat of a hobby).


  
  Will an Academic Journal require me to submit evidence that there is no workplace-conflict as an Independent Researcher?
  


The short answer is no. The long answer is that many journals would require you to disclose if you have any conflicts of interest that would affect the validity of your results. For example, if your paper is about the effectiveness of a particular algorithm used at Uber for matching riders to drivers, and you work at Uber, you would need to disclose that as a conflict of interest. However, as you have already said that your research topic is unrelated to your work at your job, it probably would not constitute a possible conflict of interest.

Submitting evidence would be even less likely, I wouldn't worry about that unless asked.

However, note that you will have to choose an affiliation when you submit, which means you probably will want to think about how you want your name to be listed. This is just for informational purposes. Perhaps you can be listed as affiliated with your company, or maybe you can arrange to have no affiliation.