Karn has at least two loyalty counters on it.

Activate Throne of Geth by tapping it and sacrificing Ugin's Nexus.
Ugin's Nexus is exiled instead of being put into your graveyard, causing you to take an extra turn after this one.
Resolve the Throne of Geth ability, putting a loyalty counter on Karn.
Activate Karn's second loyalty ability by removing two loyalty counters from it, returning Ugin's Nexus from exile to your hand.
Move to your next turn.
Cast Ugin's Nexus by paying .
Flux Channeler triggers, putting a loyalty counter on Karn.
Repeat.