Being asked to review a paper in conference one has submitted to As stated in the title (an IEEE conference). Does this create a conflict of interest antithetical to the reviewing process? Is it possible that accepting or refusing to review could jeopardise the chances of one's own paper being accepted?
No, there is no conflict. Your advice will be backed up or not by other reviewers. Likely the conference committee already knows that you are also a submitter. 

But if you want double assurance of this, just send a note to the program chair that you have also submitted. If they see any issue, they will deal with it. 

Just give an honest review as you would in any case. And trust that your paper will be accepted or not on its merits. Of course, there is quite a lot of competition, but that is always true.