Because a barbarian is still flat-footed, he just gets to keep his dex bonus to AC while being flat-footed. Uncanny Dodge does not negate "flat-footed" conditions, it just negates the loss of Dex bonus (3.5 PH, pp 26, Barbarians Uncanny Dodge).
As for Iaijutsu focus, OA page 82 only states in can be used in attacks against flat-footed opponents, such as during a surprise round, a charge attack, or during a full-attack action. It does not say only on the first strike. That applies only during a formal duel. Even then look at the second paragraph of the strike phase. It has the phrase (usually a single attack). This also infers that an Iaijutsu Master PrC, which my character is, can use One Strike Two Cuts in a duel, as well as our 10th level ability Strike With no Thought.
So in a duel, or in a combat in which my opponent(s) is still flat-footed, my Iaijutsu Master/Samurai is very deadly. After that advantage is over I am pretty much an "average" fighter. This is when my crab companion's damage dealing tank status comes into play.
Since I fought that Barbarian in a non-Iaijutsu duel, but beat him badly on initiative, I was able to use my Iaijutsu focus on him. I rolled well enough to get 8 dice of damage. Combined with my Cloak of charisma giving me a +6 damage to each bonus dice of damage, My gloves of Strength giving me a total of +6 strength modifier, and getting a whole bunch of attacks on that barbarian bad-boy before he could even swing, he died before he could even start to swing his greatsword.
Why did he duel my character? Because his clan honor demanded it. Especially after he agreed to the duel conditions and the Barbarian clan we were aiding agreed to let us insult him by offering up our "female" Crab Samurai as his opponent. He then demanded she name a second. She named my character, who doesn't wear armor. He was again insulted by the fact that I faced him wearing no armor (it insinuated that I considered him a "no threat", so I needed no armor to protect me from him). However, he allowed some common sense to prevail and decided that there may be some serious unknown factors going on in our duel. So he let it stand and started the fight. I won initiative and he died.
Too bad this happened in the barbarian lands north of my ancestral Dragon Lands. It would have added greatly to my reputation as an Iaijutsu Master since this barbarian also rode a european type red dragon as a mount. Unfortunately, (probably fortunately) the dragon turned down my offer to come live in my homelands as an honored guest of my people.