Recently I took my XF 105 & XF 305 on a shoot in a concert setting. The stage was lit primarily in an amber color (i.e, people looked reddish).

I held up my large white reflector under the stage lights, and did the custom white balance on both cameras. The both came up with 2000K; the 105 continue flashing the color temp at a slow speed, and the 305 showed it in gray.

According to the manuals: "Very rarely and depending on the light source, the (flower icon) may keep flashing (it will change to a slow flashing)." That's not very helpful as to what this means.

I assume it's trying to tell me something about the quality of the light - i.e, it's probably outside the range of what would be considered "warm" or something?

It wasn't a problem; the footage came out beautiful, but I'm just curious as to why it was doing that.

I think it means that it hasn't quite locked onto what it thinks is the right setting - maybe an out of range thing - but the manual does say the 'the results will still be better than Auto WB. Sounds like your experience bears that out.

Out of interest, what gain did you have to use? I've not yet used my 300 with a lit stage, and the low light situations were I have used it, were really quite noisy. I'd guess I was shooting in light rather lower than your concert setting though.

My XF 105 was running at 12db gain, at F 3.7 on a wide shot, and my XF 305 was running at 18db at F 3.7 on a medium shot.