Flat extension cords under rugs are not safe.

No, and you shouldn’t do it.

Flat cords are marketed as “carpet safe,” but no extension cord is designed to be run under a rug. The issue is heat buildup — even a cord carrying moderate current gets warm, and rugs (or anything insulating) trap that heat. Over time, the insulation can degrade, leading to shorts or fires. Plus, foot traffic crushes the cord, eventually damaging the conductors inside, and you won’t notice until it’s too late.

The better solution is to rearrange furniture so you don’t need a cord crossing a walkway, or use a floor outlet if you’re handy. If you absolutely have to run a cord across a rug, use a cord cover designed for that purpose — it’s a hard plastic channel that protects the cord and dissipates heat. But honestly, you’re better off just avoiding the whole situation.

This is one of those “seems like a clever hack until your living room smells like burning plastic” deals.