。
She doesn't have a shred of affection.
Literal
[topic-は] affection [genitive-の] fragment [even-も] not-exist.
かけら literally means 'fragment, piece, shard' — a tiny broken-off bit of something. Pairing it with も in a negative sentence creates the idiomatic 'not even a shred of X' expression, a forceful way of denying the presence of some abstract quality. The genitive の links 愛情 ('affection') to かけら ('fragment'), giving 'a fragment of affection.' This pattern (concrete physical noun + も + ない) is a productive way of saying 'not the slightest bit' — compare 涙のかけらもない ('not a hint of tears'), 良心のかけらもない ('not a shred of conscience').