I don't see how that could be a business case for them. Their main revenue stream is shipping fees. If you want to make a subscription with them, it's because the subscription is cheaper than the sum of shipping cost they would otherwise participate in. Amazon's gain is that you buy more stuff from them. DHL has per-delivery cost and would lose, not gain, from more free deliveries.
Flat rates work where the handling cost is small compared to the system cost. Not so here.

Also each seller would need to include "free shipping to flat rate subscriber" in their options. And only part of the "shipping price" pays the parcel service, the rest is internal handling, packaging material or profit. Replace it with zero, the seller loses as well.
Now, don't let me go into liability. Who is the customer of the shipping service, the seller or the recipient? In case of shipping damage, do you need to sort it out with DHL instead of leaving it to the seller?

@KarlE I think the business case is having a safe calculatable income they could do annual subscription etc. and people would maybe use them more in the first place (instead of Amazon's own shipping services).
But yeah I'm not sure whether there's much profit to be made ._.