How to prevent iPhone SE from always uploading burst photos?
Well after an hour on the phone with Apple support, 2 phone restores and 1 iOS upgrade, we finally got to the bottom of this.  Turns out the feature (to disable uploading of burst photos to PhotoStream) DOES work as intended.  It's the wording of the feature description that is more than a little confusing.

The text below the feature states:


  Only favorite Burst Photos will be uploaded to your Photo Stream


The trouble is, to me (and to the techs at Apple that I spoke to), that sounds like no part of a burst photo will be uploaded until you have chosen one of the photos in the burst, as a favorite.  This is not so.  What it actually means is that the entire burst will not be uploaded.  But if you have Photo Stream turned on, a single photo from the burst WILL be uploaded.  And unfortunately, it's not the first frame.  I'm actually not sure what criteria iOS uses to decide which photo to upload, but it seems to be the first photo that it thinks is "the best" somehow.

So, the bottom line is that Photo Stream is an all-or-nothing proposition.  Either every photo you take (including a single frame from any burst photos) will be uploaded, or nothing will be uploaded.  There is no way to selectively upload photos on a case-by-case basis, unless you either leave Photo Stream off and manually share photos you want in your stream every time, or turn Photo Stream off &amp; on between each photo you don't want to upload... but then you lose and have to re-download all your photostream content each time.  Not a real great solution either way.

I feel Apple should re-word the description of this feature to make it more clear what the expected behavior actually is, but I won't hold my breath on that.