Rashford, 28, returned to the starting lineup for last weekend's 5-3 win at Real Betis after four matches out of the side, but was again left on the bench for the 2-1 Champions League victory against Eintracht Frankfurt in midweek.
However, Flick was impressed with Rashford's response to being named among the substitutes for the Eintracht game, with the England forward then delivering when he came on in the second half, setting up the equaliser for Jules Koundé in the win.
"When he's on the bench, it shows also we have a good team," Flick said ahead of Saturday's LaLiga game against Osasuna when asked about having to leave Rashford out in recent weeks.
"In this position we have excellent players. What I can say, he's an absolute professional player. His attitude, mentality is great. In the beginning, he had to adapt a little bit, but now he's on his best level.
"I speak with the players when they're not playing, explaining why, and what he said to me the last day, was 'Boss, you don't have to tell me this, it's only about the team. We have to win three points, nothing else is important.'
"It's the right attitude. The mentality he has is fantastic and I am really happy he is here."
Rashford, who is on a season-long loan from Manchester United, has scored six goals and provided 11 assists in 21 appearances for Barça this season.
Prior to the November international break, he had started 10 successive games for the LaLiga leaders, but his minutes have been reduced since Raphinha's return to fitness.
Flick also has a selection headache in the striker position, with Ferran Torres and Robert Lewandowski both competing for the No. 9 role in the team.
Torres has netted 13 times in 20 appearances, while veteran Lewandowski has scored eight goals in 17 games, with Flick saying the internal competition between the two is driving them both on to deliver their best performances.
"It increases the ceiling of every player when there is competition in the position, like with Ferran and Lewy," the German coach added.
"It's good for the team; it's good for them to play at the highest level. What I can see in the last five weeks, it's amazing. Lewy, Ferran, it's perfect. For me, it's perfect."
One area where there are no doubts is in goal, despite the return of Marc-André ter Stegen from injury, with Flick saying Joan García, a €25 million ($29m) summer signing from Espanyol, is first choice.
"Joan is No. 1," Flick made clear. "There is no idea to change Joan. Joan is No.1 and he made it really, really good."
With Wojciech Szczesny currently the established backup to García, it leaves fit again Ter Stegen in a difficult position as he aims to be Germany's No. 1 at the World Cup next summer.
Reports suggest he may have to leave in January -- either on loan or a permanent basis -- and Flick confirmed he has held talks with him about his role in the team and his future.
"Of course I speak with him, it's my job to speak with the players, but it's between him and me," he said.
Barça host Osasuna on Saturday at Spotify Camp Nou with the chance to open up a seven-point lead over Real Madrid, who play Alavés on Sunday, if they can make it seven wins in a row since losing the Clásico to Los Blancos in October.
