Here's my experience:
The biggest problem in starting to ride fixed is that my brain would forget I was riding fixed, I'd come across a decent stretch of road (or a corner), and would attempt to coast. All totally subconsciously.
With flat pedals, provided I was doing a decent enough speed/cadence, I'd end up having to take my feet off the pedals until such time as I'd slowed the bike enough to get my feet back on and essentially regain control of the bike. Timeframe possibly 10 seconds during which the only real control I had was to steer and brake.
In clipless pedals, however, because my feet are attached to the pedals, as soon as my brain says "coast", my feet say "whoaaaaa". My brain then kicks back in and because I am still attached to the pedals I can just recover, easy as. And the timeframe here is just a fraction of a second.
So for my money, and assuming you do have a traffic-free environment in which to hone your skills, I'd go clipless straight away.
In traffic, I prefer flat pedals, just because I might want to put my foot down, like, now. But this of course is a preference thing rather than a technique thing.
btw, even though I've had a fixie for a couple of years now I still fall into this trap. Right now I'm probably only getting the fixie out once a month (compared to riding geared bikes several times per week), so there's an element of readjustment every time I take it out.