The downside of having a non-phone device is that it is not Google certified and out of the box does not have Google apps such as Gmail, YouTube, and most importantly, the app Market. I finally got around to finding a way around this and was successful enough to have Flash 10.1 running within minutes.
The magic is gapps4archos.apk. A link for downloading it is in the forums on archosfans.com. Because the forum post specifically talks about firmware 2.0.54 and I had already upgraded to 2.1.04, I did not have high hopes that the app would work. Regardless, I downloaded the file to my PC. After turning off application debugging via USB on my Archos 32, I connected the USB cable between it and the PC. The Archos showed up as the E: drive in Windows. I copied the downloaded file from the PC to E:, ejected the E: drive in Windows, then unplugged the device from USB. I opened the Files app on the Archos home screen, found the file gapps4archos and tapped it. (Note that my device's application settings allow apps from unknown sources.) In the app, I clicked the button to install Google apps. When that was done, I rebooted the Archos (held the power button down, choose Power Off, then Reboot). When it came back up the home screen had Gmail, YouTube, the app Market, and others.
I first ran Gmail, entered my Google account information, and was soon synchronizing data and settings between the Archos and Google. I then started the Market app, searched for "Adobe Flash" in the market, and chose to download Flash 10.1. When that download was done I started the Browser app and went to addictinggames.com. Success. To test Flash video streaming, I went to crackle.com and was watching a trailer with just a few taps. I was able to rotate to landscape orientation and push the Flash player to full screen mode. OK, on a 3.2" screen, it was not an amazing cinematic experience, but it was extremely gratifying nonetheless.