No, Winkbed mattresses do not contain any fiberglass. This information was provided directly from Winkbeds Customer Support chat.

Fiberglass is sometimes used in mattresses as a cost-saving fire barrier. While fiberglass is an effective fire barrier it may also pose health and safety concerns if it leaks outside of the mattress.
What Does Winkbed Use For A Fire Barrier?
The WinkBed and GravityLux use an all-natural fire barrier that is made from a blend of cotton and rayon. The EcoCloud Hybrid uses a natural wool fire barrier.