No. You're mixing in a different definition of "platform" here to include hardware profile. A flash app designed to run well on one mobile device will probably run well on other mobile devices with little or no modification. On the other hand a flash app designed to run well on a desktop probably is not going to run well on mobile hardware. But then probably neither will any app built on any technology that was designed to make use of desktop level hardware.
Well, it's interesting to see my comment sink down to negative territory. Here's the exact quote from Narayen in the linked article:
> The value proposition Flash has is that we allow people to author programs once and get them to as many devices as possible
He says "devices", clearly indicating that he is arguing the value proposition is to deploy across multiple phone (or mobile device) platforms, not some kind of write-once-run-anywhere proposition that works across desktop and mobile.