I'm starting to suspect there is a client side flinching mechanism as well. In other words, when you're in the flinch animation, the client will not send any commands you give to the server.
Example:
The server sees you get hit at time t = 0 ms. It sends a flinch command to your client.
While the packet is en route, the flinch occurs for 50 ms on the server than ends.
The packet reaches your computer at t = 100 ms. Your computer begins the flinch animation.
Your client prevents you from doing anything for 50 ms to simulate the flinch.
You effectively flinched twice from one hit: From 0-50ms and from 100-150ms.

The reason I think this is true is because when fighting really fast shield-cancellers, there are moments where my attack animation doesn't trigger moments before I am flinched. At the same time, any attacks made during the flinch also never triggers.
ie. I spam the attack button repeatedly in a time interval a brief moment before the flinch up until the flinch completes and no attack animation was ever triggered.
Unless the server flinch is somehow longer than the client flinch, I think the only plausible reason is there's actually two flinch effects.

Has anyone else noticed this or am I just crazy? It would be nice if someone could get this on video with a cam directed at their fingers as well.