Losing your Dexterity bonus to AC is one of the effects of becoming flat-footed:
A flat-footed character loses his Dexterity bonus to AC (if any) and cannot make attacks of opportunity.
(SRD, Condition Summary, Flat-Footed)
But there are other ways to lose your Dexterity bonus to AC, without becoming flat-footed. They are not the same thing. While this was certainly always the case, Rules Compendium has the clearest statement of this fact that I could find:
Sometimes you can’t react to a blow, so you’re denied your Dexterity bonus to AC, but any Dexterity penalty still applies. You lose your Dexterity bonus when, for example, an invisible opponent attacks you, you’re climbing, or you’re stunned. Being caught flat-footed at the beginning of combat is also this sort of situation—see Flat-Footed, below.
(Rules Compendium, pg. 15; emphasis mine)
This makes it very clear that being flat-footed is just one of several ways to lose your Dexterity bonus to AC.
The distinction is important for a number of reasons, including:
Uncanny dodge makes one immune to being flat-footed, as well as lets you retain your Dex to AC against invisible attackers, but not to other ways of losing your Dexterity bonus to AC.
Being flat-footed prevents attacks of opportunity and immediate actions; losing your Dexterity to AC does not.
Several abilities require that your target be flat-footed specifically (such as the hand of death you mention), while other abilities require merely that the target not have Dex to AC (e.g. the Complete Adventurer ninja’s sudden strike).
While flat-footed is generally the rarer/more serious condition, ninjas can make sudden strikes against barbarians because there are other ways to deny Dex to AC even if the barbarian’s uncanny dodge makes them immune to the flat-footed condition.
Most relevantly to this question, a creature is either flat-footed or it isn’t: there’s no way in the game to be flat-footed with respect to one creature and not with respect to another. For a creature to be flat-footed, there has to be something wrong with that creature’s ability to respond to any situation. Major examples include not being aware that one is in combat at all (vs. knowing you are in combat but not knowing precisely where your assailant is), or when balancing on some slippery surface (and not being able to avoid blows even if you know they’re coming because you cannot safely move around).
But you can lose your Dex to AC with respect to one attacker and not another, for example, you can have your Dex against a visible creature but not against their invisible ally.
Thus, on this:
The SRD mentions that if someone is attacked while the attacker is invisible, he's denied of its Dexterity bonus, but does not specify it's flat-footed (even if, logically, it should)
I have to disagree: no, it should not. The target in this situation is aware that a threat exists, and has their guard up as best they’re able under the circumstances. That is very different from the situation that flat-footed describes, where they do not (or cannot) make any attempt to defend themselves at all.
Anyway, yes, this does mean that cloak of deception cannot enable the use of hand of death. Hand of death is mostly limited to the first round of combat, and then only against targets whose initiative you’ve beaten. Note that a swordsage is in a good position here, however: because they ready so many maneuvers (and their recovery is so atrocious), they’re unlikely to use any maneuver more than once in a fight (so the fact that you can’t use hand of death again after that first round doesn’t matter so much), plus as a lightly-armored character with the quick to act ability, their initiative should be pretty good. Plus they have decent stealth skills to enable surprise rounds and thus more opportunities to strike flat-footed opponents.
Honestly, the biggest problem with hand of death isn’t the flat-footed requirement, it’s the fact that so many creatures are immune to paralysis, and/or have gigantic Fortitude saves.