It's almost impossible to project 10 years into the future because there's just so much turnover in the NHL due to the salary cap. The only player that was even in the Flyers system in 2010 that is still here is Giroux and that's only going back 8 years. I think it's a little more fair to look forward to 5 years from now and expect to see at least the core of this team pretty similar to today.
As for their roster situation, I think they have to be looked at as around top 5 for likelihood of success over the next 5 years. The only thing that concerns me is that IMO the Flyers pretty desperately need at least one of Patrick, Konecny, or Frost to turn into a legit superstar that can put up around a PPG pretty consistently and they also need a Robin to that Batman who is consistently at least a 70+ point guy. This probably isn't the year for Hart and even next year I think he's a split starter. So if the window begins to open next year and is fully open and they are contenders by '20-'21 when Hart is established and all the D have at least a couple seasons of experience that when Giroux is 32/33, Voracek is 31, and JvR is 31. I know those guys aren't technically old and I think there's a good change they are all still very productive players but we're more likely seeing Giroux and Voracek as 65-70 point players at best by then. In my mind I think their absolute best chance to win the Cup is in 2020-21 and 2021-22 when Giroux, Voracek, and JvR are all still on the team and the young guys are hitting their primes. After that, who knows what happens with Giroux when his contract expires. Obviously there will be a new core after that and new players drafted but as the roster currently sits today I think those 2 years are their best shot at winning the Cup.