Paint falling into engine?

I wouldn't worry. The engine has a filter to catch this type of debris. It will be caught and removed at your next service.

Small paint flecks aren't going to destroy your engine, but there is a small possibility they could do damage or a large fleck could block oil flow. I wouldn't ring alarm bells because of this, but I wouldn't leave it either.

There's 2 ways you can get rid of the paint on the threads.

1. The best way is to remove that cover and brush, scrape and dissolve that paint off the threads and the top where the cap may rub, then replace the cover. That's more work, but it means you will get the paint off without any more of it going in your engine
2. You can also remove the paint with the cover attached, there is the risk some of it will fall into your engine and cause a problem. If you decide to remove the paint with the cover in place the way I'd go about it would be to soak a rag in paint thinner and press it up to the threads. Pressing it against the threads will let the solvent do the work and will knock less paint off into your oil

This might take some time but what I would do is use a vacuum with small adapter like crevice tool and slowly pick away at the threads to remove the paint sucking up all that you pick at. Unless you remove the item completely. I would pour a quart or so of oil through it maybe picking up paint and taking it to the oil pan. Then I would change the filter and oil Just an idea! Leave the threads bare, don’t repaint! Just a thought!