Trevor McCauley did the hard part years ago, as is often the case, but it seems like there's no source code out there showing text along a path in Flash using actionscript 3. I'm not the only one thinking about this – the degrafa folks have got the extremely capable algorithmist Jim Armstrong looking into the problem too.
I don't have time to write a full explanation tonight (packing calls, tomorrow I'm in Montréal for Design Engaged), but I've got a quick solution which might be of use to you if you googled upon this page. Read on for more if you're interested in a quick overview.
(This post is part of the series I threatened to write about actionscript 3.)
For the mySociety travel time maps I wanted to have user-defined labels that looked pretty much like the map styles in the OpenStreetMap base maps we were using, like this one:

It turns out Flash doesn't have a way to draw the outlines of text easily, nor does it have a stroke filter like Photoshop. I tried a few different solutions that didn't work out, including a combinations of ConvolutionFilters (too hard to get right), GlowFilters (too blurry) and stacks of offset BevelFilters (nasty looking edges). Since the only thing in Flash that has the same quality antialiasing as the text does is, well, more text, that's what I ended up using. It looks like this:

I've included a sample SWF and pulled out the relevant AS3 code (for Flex Builder) in the full post, below.
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