How to execute script from container within another container?
As far as i understood, you are trying to take your local implementation, which runs on your pc and put it into two different docker containers. Then you want to make a call from the selenium container to your container containing the flask script which connects to your database.
In this case, you can think of your containers like two different computers. You can tell docker do create an internal network between these two containers and send the request via API call, like you suggested. But you are not limited to this approach, you can use any technique, that works for two computers to exchange commands.
I have a contanarized flask app with external db, that logs users on other site using selenium. Everything work perfectly in localhost. I want to deploy this app using containers and found selenium container with google chrome within could make the job. And my question is: how to execute scripts/methods from flask container in selenium container? I tried to find some helpful info, but I didn't find anything. 
Should I make an API call from selenium container to flask container? Is it the way or maybe something different?