Linkage or IT NEVER HAPPENED
But seriously, while I'm certainly not denying that the writers could push Karen in that direction (I'd been hoping the same for much of Season 1 myself, particularly if it helped keep her from doing an Athrun and jumping on the Suzaku bandwagon), most of the evidence of a romantic "relationship" consists of stuff like her getting erabarrassed while naked/in a bunny suit (good lord, what's wrong with her?) or moments where she relaxes while feeling that Zero is trusting her.
That last part is understandable enough:
Together they're going to achieve something she's been dreaming of for years.
She's one of the original Black Knights.
She's Zero's most valuable military asset.
She's now one of the only people in the world who's in on Zero's big secret (his identity).
She was instrumental in returning him to action so that the rebellion can continue.
It's not exactly surprising that she should feel a little closer to Lelouch than the others. Hence her reaction upon learning about the CC/Lelouch switch in this episode: resentment. She thought she'd earned a place in Zero's inner circle, but the inner circle still only includes two people: Lelouch and CC. She's still on the outside looking in, even with all she knows and after all she's done.
Or she's just mad because CC's getting ahead of her in the race to jump Lelouch's bone first. But there'd better be some actual development in that direction first, because "ZOMG SHE FITS GENERIC ANIMU CHARACTER ARCHETYPE #375, THIS IS SO OBVIOUSLY A SIGN OF WUUUUUUUUV" isn't good enough.