Would a character or creature with total concealment (that can see foes clearly) attack flat footed armor class with every attack?
To answer the question in your post:
Strictly by RAW, no, they would not.
First problem: Flat-footed only happens at the beginning of the fight - if your opponent is flat-footed when it's your turn, ALL of your attacks go against his flat-footed AC. Once an opponent has a turn, he is NEVER flat-footed again during this combat. I'm sure you meant to ask "would the opponent be denied his DEX bonus to his AC?". It's not the same thing as being flat-footed.
Second problem: nowhere in the rules does it say that Total Concealment makes your opponents lose their DEX bonus to AC. It might seem rather obvious that they should, but the rules don't say they do.
So, to put that together, if your opponent has already had at least one action during this fight, he is not flat-footed anymore. And if you have Total Concealment, you get no benefit when you attack him - but, when he attacks you, you get the full benefit of that 50% miss chance.
That's RAW.
Just about everybody, including the developers, plays it your way (having Total Concealment causes foes to be denied their DEX bonus to AC).
If you search this forum, you'll find countless discussions on this, and if you search for Jason Bulmahn's comments about Total Concealment and Sneak Attack, you'll find where he admits that this was left out of the rules. But to this date, it hasn't been put into the rules.
To answer the question in your Subject line:
(note that attacking with the foes being denied DEX modifier to AC is very much different than "auto-stealth")
Total Concealment does not make you automatically succeed on a Stealth check. Concealment and Total Concealment (along with Cover and Total Cover), are situations that ALLOW you to try to make a Stealth check.
Normally, you cannot even TRY to roll a Stealth check unless you have some kind of Concealment or Cover, so you might say that NOT having one of these situations = auto Stealth fail. You must fail if you are not even allowed to roll the check.
Getting one of these situations, including Total Concealment, lets you roll your Stealth check. But Stealth is opposed by your enemies' Perception and they always get to make a check to perceive you, even when you have Total Concealment.
Remember, Stealth is not just about vision, it is about sound, motion, smell, etc. And Perception is also about the same things. So even if you have Total Concealment, your enemies might hear you moving, or feel the breeze as your body move the air around you, or smell you. Or maybe even just a lucky hunch, the hairs standing up on the back of their necks, whatever.
So no, Total Concealment does not equal "auto stealth".
Raw you need to hide and total concealment gives you +20 or +40 to your stealth. Everything else DM Blake already covered.
I think you're thinking of Invisibility.
Total Concealment is not Invisibility and does not grant the same bonus that Invisibility grants.
By RAW, Total Concealment gives you ZERO bonus to your Stealth check (or to the Perception DC).
Again, I think most people play it like Total Concealment = Invisibility and grants the same benefits, but that is a house rule that most of us use. It's important to know when it's a rule, and when it's a house rule.
The Problem is also how to detect someone with total concealment.
You can still hear them.