I have seen banding in cases where color changes are extreme, like an intense clear dawn sky - even without any added post-processing. Drove me crazy the first time I encountered it. I almost stopped taking dawn pictures because of that.
In the case where it was not present in the original raw file but showed up after adding layers, the first line of defense is what you have already done, i.e. flatten the layers. To do so non-destructively, you can simple make a new merge layer on top of the individual layers which you will still have access to later. If this merging takes care of the banding then the problem is related to how Photoshop approximates the effect of each layer but not intrinsic to the final file. If you still see banding after merging the layers, you can try converting your final file to a 8-bit one which will introduce dithering that could help as well. Same result if you convert to jpeg.
If none of this works or it shows up in the print, then introduce noise (filter>noise>add noise) in the problem area on the above-mentioned merge layer (making it a smart layer would allow you to play with amount.) In my experience 2-4% noise levels dramatically alleviated the banding. If still not good enough, desaturate the colors. Or as I did in one of my most egregious case, covert it to black and white and pretend like that was what you wanted to do all along