I am going to consider a number of scenarios, working my way towards, and then past, the scenario you have in mind. I’m answering this way because I want to ensure that my analysis remains consistent across all of them, because internal consistency is important to any rules-as-written analysis.
Wracking touch alone, conditions do not trigger sneak attack
That is, using wracking touch on a target that has its Dex bonus to AC, and is not flanked. Simplest case, a single application of sneak attack per the spell’s description.
Wracking touch alone, conditions trigger sneak attack
That is, using wracking touch on a target denied its Dex to AC or flanked. Now this touch qualifies for sneak attack twice: once because the spell says so, and once because sneak attack itself says so, in conjunction with the weapon-like spell rules from Complete Arcane.
The question here is whether or not wracking touch’s effect that adds sneak attack damage considers that damage a bonus, or if that damage is effectively part of the spell’s “base damage.” This matters because, as two bonuses from the same source, the two applications would not stack.
I’m coming down on the side of wracking touch considering it bonus damage even from within its own effect: after all, sneak attack as a class feature applies bonus damage, that’s what it does. When wracking touch talks about “deal[ing] sneak attack damage,” is must be talking about a bonus because that’s what “sneak attack damage” is, a bonus. Moreover, the spell description itself makes a distinction, saying “The creature still takes the spell damage even if it does not take the sneak attack damage,” strongly implying that the sneak attack damage is not considered part of the spell’s base damage, and instead is a bonus. If that’s case, the two bonuses do not stack, and this ends up the same as when conditions did not trigger sneak attack—which the spell hints at by using “even if.” Conclusion: single application of sneak attack.
Wracking touch channeled through weapon, conditions do not trigger sneak attack
That is, using duskblade or spellsword or a spell storing weapon, but not combining any of these factors, to attack a creature neither denied Dex to AC nor flanked. Weapon damage is dealt, but since sneak attack’s conditions are not met it receives no bonus, and then wracking touch is applied, and due to its own wording, sneak attack applies to it. The result is a single application of sneak attack, specifically added to the wracking touch effect.
Wracking touch channeled through weapon, conditions trigger sneak attack
Same as above, still not combinining multiple channeling effects but now our target is denied Dex to AC or flanked. As a result, the initial weapon-strike qualifies for sneak attack damage, and gets it, and then the wracking touch effect also qualifies for sneak attack damage (twice, actually, per the second scenario, but again only one applies).
The question here becomes, is the wracking touch effect adding bonus damage to the weapon attack?
At this point, it becomes necessary to visit the wording of these individual channeling effects.
Spell storing weapons: “the weapon can immediately cast the spell on that creature as a free action” clearly indicates this is a separate action and effect from the attack.
Duskblade’s arcane channeling: “the attack deals damage normally; then the effect of the spell is resolved,” which is less explicit than the spell storing weapon, but nonetheless strongly implies that the spell is treated as a separate effect.
Spellsword’s channel spell: “The channeled spell affects the next target that the spell sword successfully attacks with his weapon,” which unfortunately is not very clear at all. Still, the spell is a separate thing “affecting” the target, so I would still say that this is separate.
Raumathari battlemage’s channel spell: “As a free action, a Raumathari battlemage can cast a spell through his melee weapon (usually his sword) as he attacks with it,” which is rather similar to the way spell storing works, with one key caveat: the spell he casts is cast through the weapon, not on the target. However, “A channeled spell targets the creature hit by the battlemage's weapon,” which implies the spell is separate, given it is doing “targeting” at all.
So in all of these cases, the spell’s effect—whatever it is—is treated as an effect separate from the attack itself, not a bonus on that attack.
As such, we have effectively applied two separate effects that include sneak attack damage. Even if they only involve one attack, they are separate effects, and so no “stacking” is even being attempted. And so we have two applications of sneak attack.
Wracking touch channeled repeatedly, conditions do not trigger sneak attack
The scenario that you actually asked about, where you have a battlemage or duskblade or spellsword using a spell storing weapon. But the first question is, can these even be combined?
Both the spellsword and Raumathari battlemage are using a feature called “channel spell,” and even though they are quite different, name conflicts like that should already give us pause.
Further, the spellsword explicitly calls out that “A spellsword can channel his spells into only one weapon at a time,” at least until the multiple channel spell feature increases that to two—which could plausibly interfere with a spell storing weapon.
And, as already established, spell storing itself is a separate casting after the attack.
Meanwhile, the duskblade kind of inverts the battlemage approach, by having the duskblade substituting a weapon attack for the touch attack he’d normally make as part of casting the spell.
So where does that leave us? The spellsword’s channel spell and spell storing may interfere with one another, but it is unclear. The spellsword and battlemage have quite-different abilities both named channel spell, which is arguably an issue. Since the battlemage and spell storing effects involve separate (free-action) spellcasting for those effects, they should play nice with each other and the others. And since the spell is already in the weapon in the case of the spellsword or spell storing, those should play nice with any of the others as well.
Thus, you can almost-certainly get three channelings as a duskblade/Raumathari battlemage with a spell storing weapon. It’s unclear if spellsword can be added, since it may conflict with the battlemage, spell storing, or both.
And what happens if you do? Since the battlemage and spell storing each involve a separate (free-action) casting of the spell, those are definitely independent from each other or anything else, so all three of the channelings we’re sure of are independent. But even if the spellsword’s channel spell doesn’t conflict with battlemage or spell storing, it might well interfere with the touch spell that the duskblade’s arcane channeling is trying to deliver, though it is unclear.
In the end, you wind up with three, and maybe four, applications of sneak attack.
Wracking touch channeled repeatedly, conditions trigger sneak attack
This is identical to a combination of the 4th and 5th scenarios, above. We have three-to-four wracking touch effects, as well as the original hit, now all qualifying for sneak attack damage. And yeah, none of those effects interfere with the attack, per the 4th case, so five to six applications of sneak attack is what we have here.