Privacy

You and your friend should..

• create and exchange a set of Age public keys
• use them to encrypt a simple text file
• bzip the encrypted file
• convert the binary archive to base64
• embed the base64 using Pixelknot into a photo downloaded from unsplash that contains a distinct object you both agreed on (eg a windmill)
• upload the file to imgur

Now you both can privately chat with each other by monitoring imgur's latest uploads, downloading every image that contains a windmill, read the base64 string, convert it to its binary bzip form, unpack the encrypted file and decrypt it.

Encrypt what you want to say and use whatever means of transport you want.

This question is so generic with added weird statements, there are literally dozens of solutions with little research. Due to this I assume you haven't formulated all your requirements and want us to get them out of you.

Jabber with encryption is good.

Have normal friends? Signal. It just works. Have difficult/paranoid friends? See the other commenter's imgur idea.

IRC with tor or i2p should fit the bill. On mobile you can use orbot to have the tor service running in the background and then configure your IRC client to use the correct port (5050? Can't quite remember).

https://movim.eu/ (it's an XMPP web client that works on mobile also)

You can use OnionShare to host a chat instance on the Web over Tor.

Use Signal. It's pretty secure and private and the best thing about it is that it's also FOSS!

This is the only one I can think of ATM that runs in the browser: https://github.com/positive-intentions/chat

Distribute a codex to your friends by hand, then use it to talk on any platform