I've been using Hello Talk for over two years, most people that started a conversation with me, said something along the lines of:
こんにちは、XXといいます。よかったら、英語を教えてくれませんか?
Hello, my name is XX. If it's ok for you, can you teach me english? (ofc you'd switch for japanese here)
But that's more if you are asking for help, in your case sounds like you are rather offering help or wanting to exchange both languages "equally" right?
In that case I would say:
こんにちは、XXといいます。一緒に英語と日本語勉強しませんか?よろしくお願いします!
Hello, my name is XX. Let's study english and japanese together? Please accept me as your language partner! (It maybe sounds a bit blunt when you translate to english, but I think it's totally ok in japanese!)
Edit:
As pointed by Eric, in case you already know the person and just want them to feel free to contact/message you:
英語を練習したいときに、連絡/メッセージしてくださいね。
Please feel free to contact/message me, when you feel like practicing english.
英語を練習したかったら、いつでも連絡してくださいね。
Please fell free to contact me whenever you feel like practicing english.
Here, I believe the ね softens the "request" while still being polite.