I was recently asked about this on the macProVideo.com/Forum site that I moderate. The answer was more than a single forum entry could cover, so we are going to make a macProVideo Hub article for you all.
I originally tried with help from someone else to do this using the shape of the Particle Emitter itself, and that just became too convoluted and was a ton of work. So for now, I'm using the Image Mask technique as it is much easier, faster, and works just great. So launch Motion and follow along!
I'll take a new generic Motion project (not a Final Cut Pro X template), make it 720p24, 5 seconds long. I always rename my default group, in this case 'Main Group'. Make sure your playhead is at the start of the project.
I can do this next step in a variety of ways by using any of the shape tools, the bezier tool, or just use a vector graphic image. For this example, I'll draw my shape out with the bezier tool (the shortcut is B) draw a line, then hit Return when done. Shift-S makes the Transform/Select tool active again. Now that I have my shape, F4 to the Shape tab in the Inspector, and turn off Fill. Toe adjust this sharp edged shape into a graceful, rounded shape, I can go into the Geometry tab and adjust the roundness to my liking.
When I Command-2 for the Library, then go to Particle Emitters > Pyro > Flame Line, I'll select it and hit the Apply button. F4 for the Emitter tab and change the Shape setting to Geometry. Dragging my Bezier layer into the Shape Source image well, makes it conform to that geometric shape. And I have to remember to turn off visibility for my original shape layer.
When I start playback in the Canvas, going to the Emitters tab, I will adjust Birth Rate to 250 as a starting point, Initial Number to 250, and a scale of 200. When trying this on your own, you can adjust any other particle emitter and particle cell parameters you wish.
When the flames look reasonable along my line shape, I'll stop playback, place the playhead at the start of the project, and select the Bezier layer for my line shape. Command-D will duplicate it, and then Command-] will help me move it to be the top layer inside my Main Group.
Then I have to turn on its visibility in the layers pane. Placing the playhead in the middle of the timeline so I can see them both. In the Shape tab (F4) increasing the Width and adjusting the position of this shape layer lets me be sure the flames are covered by it. This is going to be our revealing mask.
Once I'm satisfied with my results, I'll turn off its visibility check box. Then selecting the Flame Line particle emitter layer, I'll right-click and chose Add Image Mask. I can drag the duplicated 'Bezier copy' layer I just created in to the Mask Source well.
With Command-2 I can get to the Library and go to Behaviors > Shape > Write On. Selecting the shape layer I am using for my mask, I will drag and drop it onto my Bezier copy layer. Playing my project I can now see how the mask reveals the flames with the Write On behavior style. But I do notice that the edges of my mask, especially the leading edge, is sharp and not looking correctly. I'll fix that.
Command-2 for the Library and go to Filters > Blur > Gaussian Blur, then apply it to the Bezier copy layer, also. I'll adjust the amount, at least in my test project, between 50 and 100. When doing this yourself, you are free to adjust it how ever you wish.
This is a fairly straightforward, easy and quick effect to generate. Remember to experiment with various parameters. And also be aware you can use many other of the particle emitter presets in the Library, or even create your own. This isn't just about cool flames, but about how to use an emitter on a shape, and mask it to have a progressive writing on effect. Let your imagination go nuts and have fun!