Raphinha (3), Robert Lewandowski, Jules Kounde, Dani Olmo and Ferran Torres were Barca's goalscorers.
Flick later said, "We did well from the start. It was nice. The team gave it 100% and we created chances from the start.
"The goal was to win all four games and we've done that. It seems the fans have understood that. I'm very happy. When we go out to eat, to dinner... the fans come up to us and they're very nice to me. I sense the good energy, and there's that in the team too. Everyone gives support and energy. We act like a family, and that's nice.
"I think that when you see the stadium vibrate with this victory... the fans have seen something special... the team is also, with the support of the stands, more hungry for goals. The players have not lowered their intensity, and that is good. That is what makes the fans proud. We are here to give our best, individually and collectively.
"I'm proud that they say I'm the best signing, but we're in the fourth matchday and that could change. I'm happy that the fans are happy, but we have to keep going. There's a long road ahead. We're going to try to do better in each game. Now there's a break, which will be positive for everyone, including the players, as they're going to their national teams in a great atmosphere."
On Raphinha, he added: "I think it took him too long to score a hat-trick, he has the quality and confidence to have scored one before. I think he feels freer on the pitch. Rapha is a player who does many things very well."