The hardest part was that, with the automatic rules, make insisted on deleting the "intermediate" file. But in this case the intermediate file was the swf itself. There is a ".PRECIOUS" rule that appears designed for this purpose that made no difference. After much trial, error and banging my head against the keyboard until it bled, it seems setting ".SECONDARY" to blank was the solution. Here is the full makefile (saved in a file called Makefile, in the same directory as my mxml files):
% : %.swf
This makefile is generically useful for when you want to compile and run something; especially when experimenting with lots of small individual files.