Phonak Paradise hearing aids can connect directly to Bluetooth-enabled devices, giving them the ability to receive and play streamed audio. They behave in the same manner as Bluetooth-enabled headphones.
Several manufacturers sell headphone guitar amplifiers. This one from Fender is described as The Ultimate Personal Practice Amplifier – Featuring 12 Amp Models, Built-In Effects & Bluetooth.
It has Bluetooth, but it can only be connected to wired headphones. It is a Bluetooth receiver, for backing tracks or whatever.
I found some discussions about the issue on music forums. The reason that the amp doesn’t connect to Bluetooth headphones is because of Bluetooth latency. The time lag makes the instrument unplayable.
This piece on the Guitar Gear Finder website bears this out. Under Can I connect an electric guitar to Bluetooth headphones? it states:
At the moment, there are no good options for connecting an electric guitar to Bluetooth headphones. While it is possible to connect Bluetooth headphones to your electric guitar, the results aren’t good.
The problem with Bluetooth is latency. Latency is the delay between when a signal is sent (eg: when you pick your strings) and when the signal is received (when you hear the note coming out of the headphones).
While listening to music through Bluetooth headphones is perfectly fine, trying to play guitar with Bluetooth headphones is a nightmare.
It might be possible to achieve a useable connection to the aids by plugging the amplifier into an intermediate Phonak device.