Here's the deal. Windows 8 will ship with effectively two browsers ... a standard Internet Explorer 10 that you'll do your web browsing through and a second Metro-style app. The standard IE10 will support plug-in like Flash just as it does today. However, the Metro version of the browser will not. If you're using the Metro browser and you need to make use of a plug-in such as Flash, you can switch to the standard browser and get access to plug-in goodness.
Here's the Metro-style browser:
Here's the regular IE10:
You can also switch between the Metro browser and the standard with a couple of clicks:
And if IE doesn't float your twig, install a different browser!
It makes sense that the Metro-style IE doesn't support plug-ins because the Metro UI loads in at the start ... can you imagine what sort of performance hit might occur from having to load a bunch of plug-ins? There's also the issue of security to consider.
Worried that the ARM version will not support Flash? Don't! ARM and Adobe are working closely to make sure ARM is not left behind (it's unclear if the ARM version of Windows will have the classic desktop, but everything I'm hearing suggests that it will .. we'll see).