A better place to ask is
Tablet OS SDK for Adobe AIR - BlackBerry Support Community Forums as it's specifically for Flash development on PB.
You can use either Flash Builder 4.6, Flash Professional CS5.5 or one of the free alternatives to package and deploy your app. Note that only Flash Pro has support for timeline scripts. There are free trial versions of both Flash Pro and Flash Builder on Adobe's web site.
You *should* even be able to use your old, existing Flash version to generate the .swf, then package it up into a signed .bar using just the AIR & PB command-line tools.
Or you can use WebWorks to create an HTML5 app which just embeds your .swf like on any other page.