I have a lot of data from my PhD, which I believe confuses my supervisor quite a lot. Therefore, he is hesitant to publish them for now. How can I get good academic feedback on this data without submitting it as a paper?
Talk to as many people as possible about your work
This can be in formal settings, such as a poster or oral presentation at a conference. You could also ask to give a presentation to colleagues within your department. Or it could be informal, such as chatting at a coffee break or after a seminar with fellow researchers.
It's often tempting to hold on to your work and only present it when it feels "finished", but these early stages are often the most useful ones to get feedback. So you need to be brave, and accept that there may be flaws or complications that you've not yet thought of. That's why you are doing it.
If you don't have a good feeling for the relevance of your data, and your advisor is "confused", then now is not the time to publish.
Also, "data" itself isn't necessarily what you're looking for. To quote Alan Wilcox, former editor of Epidemiology:
Data do not speak for themselves. They need context, and they need skeptical evaluation.
It sounds like you don't have that context, or that skeptical evaluation. I would suggest that the first thing you need to do is get with your advisor and come to a coherent understanding of your data before you try publishing it. An attempt to just dump data you and your advisor don't fully understand into the literature will do neither you nor the field much good.