Bottom line up front: You have wandered into a dense thicket of incomplete rules. You will need your DM’s ruling on a number of different issues before you can answer this question, and those answers will apply only to that game. There just isn’t enough detail in the official rules to give you a general answer.
First, if you haven’t already, you will want to double-check with your DM that Augment Healing actually applies to vigor-type spells: they arguably apply a fast healing condition to the creature, rather than heal the creature directly, in a way that may not actually work with Augment Healing. Furthermore, Augment Healing adds +2 per spell level to the amount of damage healed by a spell, which means as-written there’s just an extra 2 hp/level total—not 2 per level per round or even 2 per level per target, but just 2 per level. How that interacts with multitarget spells or heal-over-time spells is just not described by the feat.
The most literal reading I can think of, assuming Augment Healing works at all, is that one the first round of mass lesser vigor is that all of the creatures get fast healing 1, plus there is also another 6 hp of healing that you can dole out among the targets as you like on that first round. But even that limited reading still requires me to inject extra rules that Complete Divine neglected to specify. So you’ll want to clear this feat up with your DM before even selecting it.
Beyond that, we have the question of whether or not the shield guardian’s spell storing ability can also “store” the benefits of Augment Healing. Unfortunately, this is yet another ability that leaves out a lot of details.
A shield guardian can store one spell of 4th level or lower that is cast into it by another creature. It “casts” this spell when commanded to do so or when a predefined situation arises. Once this spell is used, the shield guardian can store another spell (or the same spell again).
That is the entire description, and it offers zero guidance on how the parameters of the spell—DC, caster level, and yes, things like feats, are handled. That depends on who the caster of the spell is—is this just the same spell originally cast into the spell guardian, including all parameters set by the original caster? If so, your Augment Healing feat ought to apply. And maybe that’s so; the rules do put “scare quotes” around the statement that the shield guardian is casting the spell, so maybe that means it actually isn’t.
Or is the shield guardian the caster of the spell entirely, using its own stats for it? If so, which stats? It’s a mindless, 1-Charisma creature, so hopefully not those. Or maybe it casts it as if it were an item, like a wand does, using the minimum caster level and ability scores?
There is the spell storing line of magic rings, which do have the same name. Maybe the shield guardian uses their rules? That specifies that spells have their minimum caster level—but still no word on how DCs are determined, to say nothing of whether the original caster’s feats or the eventual caster’s feats apply to the spell. Still, the ring at least loses the scare quotes on “cast” so maybe it’s real and true casting from the ring, and the ring’s wearer (and not the original caster) gets to apply his feats. But then that still leaves us unclear on what the quotes on “cast” for the shield guardian’s version imply.
Personal ruling: if this were my game, I would allow Augment Healing to apply to healing-over-time spells, but it would just be a batch of HP at the beginning of the spell that does not get repeated each round thereafter. I would allow each target of a multi-target healing spell to benefit, though, rather than having you divide it up by the number of targets. And I would provisionally allow the shield guardian’s spell storing to store all of your parameters—DC, caster level, feats, class features, and so on—but I would be keeping a close eye on it and reserve the right to nerf that if I felt it was becoming a problem.