"Do the rules work in my favor?"
Maybe. As per Big and Little Creatures in Combat on Tiny, Diminutive, and Fine Creatures, a creature of such a size "can attack into [its] own square if [it] need[s] to." However, "[s]ince they [creatures of those size categories] have no natural reach, they do not threaten the squares around them." Nonetheless, Attacks of Opportunity on Threatened Squares says, "You threaten all squares into which you can make a melee attack, even when it is not your turn." Taken together, a Tiny or littler creature should threaten the square it occupies (as per this (ahem) fine answer).
It's unclear when Big and Little Creatures in Combat on Tiny, Diminutive, and Fine Creatures says, "They also can't flank an enemy," whether this means either These creatures in conjunction with creatures of similar size categories can't flank an enemy or These creatures can't participate in any efforts that will enable any ally to flank an enemy. Fortunately, the feat Blades above and Below bypasses the issue: When creatures using the feat "threaten the same enemy, [they're] both considered to be flanking that enemy, regardless of [their] actual positioning," and, presumably, regardless of whether the flanking's actually occurring or not, the feat's specific text overriding the general rule.
Thus, in a typical campaign, this GM would totally allow a master that possesses the feat Blades above and Below and that shared the feat with its Tiny or littler familiar to pair up and be considered flanking that enemy—if properly positioned and if facing an enemy of the proper size. (According to the feat's benefit, for example, such a properly positioned yet otherwise typical Medium human and Tiny his cat familiar still can't be considered flanking a Large ogre, a Small feisty hotspur, or a Diminutive toad, but, at least the cat will be pleased that, using its slave's labor, it can finally be considered flanking a Tiny rat.)
However, I was unable to find Society-specific rulings on these points, making asking directly better than hoping the judge will agree with a random dude on the Internet.
"Is it a legal build?"
Yes. According to Pathfinder Society Roleplaying Guild Additional Resources (Nov. 7, 2016), a fighter with the archetype eldritch guardian that meets the prerequisites for the feats Blades above and Below and Improved Familiar—picking an azana lyrakien—is legal for Pathfinder Society play (that fighter archetype even eventually meeting the Improved Familiar feat's prerequisites according to this FAQ entry). All the sources check out.