The images you've both produced has always been the standard by which I, till this day, strive to reach. I will agree with you that the high shutter speed seems to be the most important aspect of producing those incredible solar flares but I wonder how much the depth, the stillness and visibility of the water plus the angle of the sun play in making this shot possible.
One of my best flared shot was taken in about 10ft of water while swimming with manatees...

My settings were f/5.0 and 1/320 sec at ISO 64. I remember looking through the LCD and whole thing being washed out from the bright light. I was attempting to capture the sun entirely behind the manatee but I missed it slightly.
What I've never understood was why the 5050 is able to sync with the strobe at even 1/1000 of a second while most DSLRs can not. Is it because of the electronic shutter on the 5050?
I have attempted to replicate these solar flares at depth of 50ft+ but I've have not been successful. Have any of you had any luck?
I also think my old 3040 was better at producing solar flares than the 5050.
{Just throwing random thoughts here}
Laz