Signal does not have a way to manually export your private keys and chat history, but the process of "moving" your signal account to a new phone is quite straightforward. You put both devices on the same wifi/LAN layer 2 broadcast segment, start the transfer process in the app, input the verification codes displayed on the screen from both devices, and it sends everything over. This moves the private key in a way that does not result in all of your contacts receiving the scary "this person's key has changed" message.
"Moving your account" is not what i talk about, besides not being possible between android and ios with history. User agency means a user is allowed to access his data and do what they want with it how they want, realtime and with whatever code they want to write to do so.