He couldn't tolerate even the slightest insubordination from his subordinates.

Literal

Subordinates [possessive-の] insubordination [topic-は] how-much small things [even-でも] tolerate could-not.

不服従 means 'insubordination.' どんなに小さなものでも means 'no matter how small.' 我慢できなかった means 'couldn't endure.' Describes a strict authority figure.