A bit of an update:
I have trimmed the project down to bare plain black 5 seconds and text and resaved this. I have also changed my premiere cache folder to my scratch SSD drive. Closed and reopened the file - and it is now seeming to work - I can drag the marker in applied effects and it is hesitantly doing the same in the time-line.
Also I have changed my technique in applied affects brightness to moving the timeline then clicking the key-frame then changing the brightness (I am sure on a pc I can move the timeline change the brightness then click the keyframe to remember the spot...)
Also I am rendering the project after EACH change - a bit tedious but it is hanging together now.
This is a bit odd - I am using a Mac Pro 3.04 GHz 6-core 2012 machine. It is a pretty pro machine (not the new trash-can but should be good enough). Am thinking there is a cache problem. I am thinking of upgrading elements 11 to 15 but would rather spend the money on final cut if this is a problem... (appreciate help here)
I was not able to duplicate your issue, Richard. Version 11's Lens Flare brightness keyframed perfectly for me on El Capitan.
However, there is one difference between my workflow and yours.
Your black background is a blank BMP. Mine is a black video clip produced by going to the Project Asset's panel's Panel Options (Upper right of the panel) and and selecting New Item/Black Video.
I don't know if that makes the difference, but it might be worth your experimenting with.