Welcome to the T&TH site. It's a great place with lots of good folks who are always willing to share their experience and help.
I started shooting Federal Flitecontrol Wad shells in early 2005 and have shot, conservatively, hundreds in both lead and Heavyweight. You might be interested in an article that I just re-published about my tests of that shell http://allaboutshooting.com/article_info.php?articles_id=290
I've had a number of inquiries about the Flitecontrol Wad shells since Federal introduced the 20 gauge loads this year.
To answer your question directly, you should have no problem whatsoever with those shells through your fixed full choke gun. That full choke should be .690 and chokes with .670 do give the best results but I've had folks with factory full chokes get good results as well.
I would suggest that prior to shooting that shell, you really "deep clean" your barrel. That way you should be able to see just how well that wad works in your barrel. Plastic or powder build up can effect any wad and seems at times, to effect the Flitecontrol Wad.
Lastly, that wad in the Heavyweight version is very thick and gives excellent bore protection. You will probably see that it travels a full 40+ yards and most will hit the patterning board at that range.
Good luck with those shells this spring.