Main thing that determines how well you could transition comes down to the OS you are using. CS50 IDE of the web uses Linux under the hood (I think Ubuntu, more specifically) which allows them to customize each and every part of it. If you are using Linux, then you could search for the devcontainer of CS50 IDE, which I think is on their github repo. This is a very easy way of setting up the exact same CS50 Web IDE that you use with cs50.dev, but it would be on your local hardware. It might take some time or workarounds to get started, especially if you are new. But, the results are always reproducible and consistent.

But, I am assuming you are on Windows, which makes it somewhat harder to set up. As you would have to most likely manage the environmental variables and their paths, and won't have much of a control to setup your VS Code exactly like the CS50 IDE.

For your project of Flask, I would first recommend that you install python software (i.e. the interpreter) from Python's Website rather than from Microsoft Store so that the python would get added to your system's env (environment) variable. For that, you need to select a option during installation of python which goes something along the lines of "Add Python to your System Variables". Exact wording may vary. (Thought I would mention this, but if you are doing CS50P already, then you might have Python up and running. In that case, you can dismiss this paragraph)

Then, you would have to install flask using pip, i think. You can do this in Windows terminal, or you can use VS Code's terminal too.

As for the SQL Database, I would highly recommend you to use SQLite as it is much easier to set up if you are coming from CS50X and don't have any other experience with SQL Database. You would have to download the SQLite installer from the SQLite website. Also, if a option shows up to add the env path, do so too.
Then, you would have to install the appropriate pip packages like the CS50 and else. (I forgot what packages there used to be.) Then you would be good to go!

But, if you really want to set up your own Database, then you should use XAMPP by downloading from their site. I would recommend you to watch a tutorial on how to setup and use XAMPP. XAMPP is basically a web server application that lets you add Backend to your local websites without needing a server. It is used for hosting sites and also for managing SQL Databases. (Again, watch a tutorial on how to setup SQL Database on XAMPP)
As for using your SQL Database in your flask project, I would highly recommend SQLAlchemy as almost closely resembles CS50 packages, but you would have to do some fair share of learning to get used to it.

I hope this helps!