What cord do I need to connect my Beats Solo 3 headphones to a guitar amp?

judging from it's page Solo³ Wireless - Everyday On-Ear Headphones - Beats (beatsbydre.com)

then it seems like that headsets only means of audio output is wireless bluetooth

so you will proably have to find a way to make the amps recieve that something like

Amazon.com : bluetooth receiver

more

bluetooth receiver - Google-

and then some adaptor that change whatever analogue connector it has to the typical jack connector of the amp

yes

for the headset to receive audio the device needs to make it's audio output into bluetooth, as I don't believe the type of headset offer any type of wired audio output.

They are Bluetooth only.

They don't support a cabled connection for sound.

The cable and port is for charging only.