I saw this problem Re: Adobe 6/CC not embedding Lens in EXIF for Flickr and saw it was supposed to be fixed.
I've just started having this issue over the last few days with LR CC 2015.6 (64bt Windows 10). Exported files seem to contain all the correct EXIF data but when the built in Flickr connecter uploads to flickr, I don't get any exif uploaded. The jpg uploads fine but flickr doesn't seem to get much more than the camera model.
I've looked at the export and publish settings for everything I can see - they all say to include 'All Metadata' but remove person and place location. These are the settings I always used with no problems until just a few days ago.
Is there still a bug?
It's a recent problem with Flickr itself, acknowledged by Flickr staff: Flickr: The Help Forum: [fixing bug] Exif info has gone missing. Flickr has gotten quite unreliable in the past year or so as Yahoo (its owner) enters its death spiral.