Hi there, depending on when you are going (maybe), and the mood of the crew when you go, the welcome is not friendly to English speakers, I am afraid to say. The last couple of times I have gone, I have sworn it to be my last. The setting can be spectacular, if they give you a good table (not so nice more recently to Americans in my experience). When I went with a friend who lives and works in Rome (as a translator, so her Italian is excellent), once she arrived, we were treated well. But before that, it was not good. The food is pretty good, but loving Rome, as I do, I think there are many nicer places to try, where the welcome is warm.
I was in Rome over Thanksgiving and wrote it up here; [Rome] Trip report in bites I share your love of Armando and Roscioli.
I would very much recommend Trattoria da Cesare di Casaletto, Colline Emiliane and Trattoria Monti, all of which I went to (and wrote about) in November, though it was the first taste for me of the latter two restaurants. Colline Emilliane is not a Roman restaurant per se, but rather the menu hails from the Emilia region of Italy. I think an excellent restaurant of that kind (still haven’t gotten to Emilia-Romagna so cannot compare it to the actual area), so I would take a look at the menu and maybe see if it appeals?
If you need a restaurant near Flavio, I could have a think…or maybe someone else can recommend?