If you are talking about mobile phones... I don't think flash is really even the issue with the type of data being displayed.
Even if your phone supports it, I don't think WDLive makes a good mobile display of the data that can be created in a format that would be good viewable on a wide number of devices. It is more designed to be on a full page browsers. It also, like on a full page, takes a long time to load. That is okay, if you have it displayed for long periods of time in a tab or on a full page... but for most mobile use when you are switching from one thing to another quickly all the time, it takes too long
Even with a smartphone that can display Flash (most non-Apple devices), it is not easy to use as you typically have to resize to get it to fit.
Another big difference is what looks good on a large screen, normally doesn't on a mobile screen. Lots of dials for example are hard to read on smaller screens where numbers are much more important.
There are already a number of people who are using web based pages for mobile output that provide similar information and look much better on multiple mobile devices (including droid and iPhones on the same page).
On tablets, which larger screens, WDLive does much better since it can be viewed at a larger size that makes it possible to view the information. However, even there, you can craft a web page to do similar information.
I don't create flash content, but I think (and I could be wrong) that if you need to support various different sizes, you would need to have a number of different versions to make them display well. Mobile displays are very limited in size, and how you craft a mobile version of something is much different than doing it for a much larger display.
Example... (
note, this WDLive page was NOT changed to better suit a mobile display):
My existing WDLive on my mobile phone portrait mode.

I can switch to landscape mode, but then the bottom of the flash display is cut off.
In both cases, I had to play with the browser screen to get it to the point where it was on the page. It also takes a long time to load, typically 20-30 seconds. A long time when you want a quick glimpse of the current weather for the station.
Since this is a mobile smartphone, you would not stay on that for any real period of time, since you are using your phone for other things. In my case, a lot of different things.
My mobile web page however is quick to load, formatted for a display (looks as good on a droid and an iPhone) makes it easy to quickly see what the temp is, hi and low, other more detailed data, loads on just about any browser and has additional tabs for more information for a more detailed look at the data.
On my mobile web page, a view for mobile is designed for mobile use.
Newer format on left, much older format on right, both are scrollable to get more infoReformatting WDLive for Mobile OutputCan you format a WDLive page for mobile use, perhaps. Would it look good on the various different sizes of mobile displays etc... most likely not.
Would be a good challenge though, however, you won't get much participation from devices that don't support flash to begin with.