I've looked through websites at kids bikes, but many don't specify very well whether they are fixed or free
, and many of the ones for growing kids are geared or at least SS/coaster. Can anyone point me toward some brands that definitely have fixed in their ranges, and cater beyond the real littlies? Do flip flop exist for kids bikes? and/or modification as alternative to trying to find fixed for a kid who is past the age of 3...
edit: and not costing huge amounts, flash materials/designs not necessary...
The Australian Standard (AS1927) recommends or requires (I don't have it in front of me) foot operated (ie coaster) brakes for kids bikes. Can't remember how they define kids bikes.
That means, to get away from coaster brakes, you're shopping for bikes that are sold purely for competition purposes, and thus are exempt from meeting the Mandatory Safety Standard (which references AS1927).
Kids competition bikes... hmmm... now you're getting into Pageant Mom territory. Parents who buy competition-specific bikes for kids aren't known for being bargain hunters, so the "costing huge amounts" clause might be a struggle .
I have seen tiny little Hillbrick track bikes, which would meet your purposes. Not sure how small they go though.
In terms of flip-flop, a BMX freewheel will screw on to any track hub, whether or not it has a stepped thread (ie designed for a track sprocket and counter-threaded locknut). My current (singlespeed freewheeling) commuter wheel is on a track hub with a stepped thread on both sides. I could screw a different freewheel on the other side if I felt like it. Or a track sprocket.
If you need a little tiny fixie, I reckon the most promising avenue would be to get a little fixie rear wheel built (on a track hub) and install it on a conventional coaster-brake kids bike (ie a BMX frame or similar). Any frame designed for a coaster brake will have horizontal dropouts, which is ideal for running fixed. I believe kids bikes run 120mm dropout spacing, which is also standard for track hubs.
Your reasoning for wanting a kids-sized fixie is intriguing...
 although, I suspect you're looking on behalf of somebody who's accustomed to paying disability support prices... and in that context, no off-the-peg bicycle will appear expensive.