I think what he's doing works like this:

Round 1: Cast Spell X into familiar's Spellblade. Total spells between two blades = 1.
Round 2: Familiar reflects Spell X into owner's Spellblade, owner casts Spell X into familiar's Spellblade. Total spells between two blades = 2.
Round 3: Familiar reflects Spell X into owner's Spellblade, owner reflects spell X into familiar's Spellblade, owner casts spell X into familiar's Spellblade. Total spells between two blade = 3.
Round 4: Familiar reflects 2 Spell X's into owner's Spellblade, owner reflects spell X into familiar's Spellblade, owner casts spell X into familiar's Spellblade. Total spells between two blades = 4.
...
...profit!!!
...
Round N: Familiar and owner stop bouncing between each other, and take N free actions to release N instances of Spell X at target enemy.