Different browsers have different implementations of HTML5 and CSS, which is what WebD uses.
Unless you went through a lot of work to create a theme and object styles for your layout, some of the flickering and refresh may come because of all the work to translate your UI design. It is currently probably littered with local CSS overrides for all objects?
The dimming of the screen that I see when logging into your DB appears to be intentional WD behavior. I see it using both FireFox and Chrome. I also see it just after I have logged in as Guest when I click on the "Refresh List" button. For me, it appears a little longer than just a flash or a flicker -- it is a brief moment of screen dimming. I attribute the extra duration to the difference in latency of our connections to the DB.
In any event, it appears intentional to me -- a way to indicate to the user "Hang on for just a second, I'm refreshing right now...".
If this is correct, and we are seeing the same phenomenon, and it is intentional behavior of WD, then it naturally leads to a few questions:
1) Which combinations of circumstances require a refresh? (i.e. combinations of DB/Layout design combined with specific user actions)
2) Are there any design techniques that I can use so as to reduce the incidents indentified in question #1?
3) What can I do to optimize the DB/Layout to reduce the duration of the refresh dimming?
Wim has already mentioned #3 above, and RC Consulting posted a great video with a clear explanation of some valuable information regarding #3 (if not also #2).
If you have not yet seen RCC's video, I highly recommend it -- watching it would be a great start for any WD endeavor.
There has been at least one other thread here on TechNet regarding the WD refresh dimming, but I do not recall that anyone has yet to post any findings that really dig into answering questions #1 and #2 above.
The link to the post with RCC's video: https://fmdev.filemaker.com/message/134683