It really isn't even possible in today's NFL for any team to be a true dynasty. That is, if you only want to count championships.
NE will remain a quality team as long as Brady and BB are around. Figure the playoffs 4 out of every 5 years, which is a very hard thing to do. They may have jumped the gun a bit, trading Seymour, etc, but they have stockpiled picks, and that is a big deal with the uncapped year coming. They are positioned with all of those picks to be a very good team for a long time.
There won't be a quality player available in FA for the next 2 years. First a team has to offer a ton of $, that the original team is allowed to match. Even if a signing team does spend too much and over pays an RFA, there is still compensation. Given that, few teams will be willing to surrender draft picks.
NE has postitioned themselves to remain atop the NFL for the next 5 years.