Do we know the processing power (in GFLOPs) of Apple's H1 chip?
Do we know the processing power (in GFLOPs) of Apple's H1 chip?

We don't, but I'll venture an estimate:

It needs to do bluetooth. You need no floating point for that.
It's not clear how much audio preprocessing it does, but let it do a bit of beamforming: that happens on the fixed-point audio samples; it might be advantageous to compute the (if used at all) singular value decomposition when estimating directions (I don't even think it does something like that), but that would happen maybe 10 times a second, and would mean maybe 1000 floatining point operations - by all means, you either do that in software, or you round your GFLOPS to 0 with an error of less than a millionth
According to the wikipedia page, it is sensitive to &quot;hey siri&quot; commands, but these are processed off-headphone. My alcatel OneTouch 511 was able to recognize spoken words (for speed dialing in the phone book), 2001. We can conclude that the necessary compute power was exactly 0 GFLOPS, with an error ranging in the parts per billion.

So, the answer is
0 GFLOPS.
This is not a device where having much floating-point compute power is an advantage. On the contrary, every transistor you flip, uses your precious battery energy; it's desirable for the device to do as little computation as possible.