Create a /SO action that will accept a question and post to SO.
Per Nathan's comment, this may not be possible but worth trying nonetheless.
https://api.stackexchange.com/docs/create-answer
This can be used to answer while in SO.
This is how we can post a question using an action: https://api.stackexchange.com/docs/create-question#tags=Julia&preview=true&filter=default&site=stackoverflow
This is how we would host the url for the slack action: https://ngrok.com
Definitely more involved to make a slack App with actions, but this seems to be a good resource https://medium.com/slack-developer-blog/tutorial-developing-an-action-able-app-4d5455d585b6