There are two factors that'll determine whether or not your phone is ready and able to run Flash, whenever it becomes available. First, you'll have to worry about software: As far as we know, Adobe is only planning on supporting Android 2.0 and up, meaning that unless you've got a Droid or Nexus One, you're shit out of luck—unless, of course, your phone gets treated to an upgrade.
But even then! Optimized as it may be, at least some older hardware could have issues running Flash smoothly. Answering a question about a specific phone, Antonio Flores, a man posting on Adobe's support forums who everyone—including a community manager there—seems roundly convinced is a legitimate Adobe employee, says:
No, the HTC Hero will not be supported b/c it does not have the correct Android OS version and its chipset is not powerful enough. We require a device with an ARM v7 (Cortex) processor. Examples include the Qualcomm Snapdragon chipsets and TI OMAP3 series.
That Cortex qualifier could be a killer, too. Even if your G1 was treated to an official Android 2.1 update, there's a good chance it just doesn't have the horsepower. For the time being, this could—again!—be a Droid-and-Nexus-only affair. (Update: To be clear, what we're talking about here is Adobe's full mobile version of Flash 10.1, not HTC's version of Flash Lite.)
Speaking of updates, there's actually a third factor that could screw your phone out of new Flash: The upgrade path. The Palm Pre's webOS 1.4 update helps prep the platform for Flash, but leaves it up to users to download the plugin as an app. On Android, the distribution system looks like it'll be even more dependent on automatic, over-the-air delivery, so if Adobe tells your carrier and handset manufacturer that your handset isn't up to the task, that too could keep you from experiencing the rich and wonderful scope of Ads That Move On The Internet, on your smartphone.