Barcelona are also in an intense push to sign Marcus Rashford. But now it's up to him, like now it's up to Rashford whether he wants to stay at Manchester United or wants to move to other clubs. The boss of Manchester United already expressed his opinion that he didn't need Marcus Rashford, and that's why I believe that he would move to Barcelona rather than stay at Manchester United. Barcelona-supporting director are on the way to meet his agent to discuss the deal.
Hansi Flick needs a natural winger, while Marcus Rashford is a precious natural winger, and indeed his move would be make sense because the Barcelona team is feeling the lack of a left winger.
I also think that Marcus Rashford will likely move to Barcelona especially because it looks Manchester United is ready to let him go. You made good points about how Barcelona needs natural left winger like him which makes transfer look like good fit for their team under Hansi Flick. Since Barcelona directors are reportedly talking to his agent it looks like move could really happen. It will be interesting to see if he actually transfers and how he plays if he does.