The Paora Winitana and Jarrod Kenny-skippered Hawks have won only three matches from eight with their offensive system coming under intense scrutiny although their defensive one has improved.
This week's double header on the road will offer the Hawks another shot at redemption with the game against the James Blond Supercity Rangers on Friday and then back to Cowles Stadium on Sunday to exorcise their Canterbury demons.
Flynn says Atkinson's role has been "outstanding" and it's been a key factor in why the Hawks have won their three games.
"Unfortunately in the other games the consistency hasn't been there and specifically in the last couple of weeks he doesn't want to fufil that role."
Flynn is of the view the 29-year-old power forward from South Carolina has been partial to the offensive transitions.
"We brought him here to be opportunistic and score when he can but we need him really for his defence and his rebounding," he says, mindful the two facets aren't mutually exclusive.
"It's nice to have that extra offence he wants to do but you can't sacrifice the we sort of stuff to have more of the I sort of stuff."
He says Nigerian import Suleiman Braimoh has always been the focal point in the offensive department with co-skipper/point guard Kenny.
Everyone else is expected to fulfil different roles and, consequently, the shooting guards will get better look-ins at the rim. Atkinson does have the licence to clean up on the offensive rebounds.
"He [Atkinson] has done a great job filling those roles in our wins but not consistently enough for the whole season."
The former Harbour Heat/Waikato Pistons centre once held the NBL shot-blocking record, averaging three a game as the sole rim protector on the Pistons squad.
Flynn has felt his disappointment since the impasse and says they have held three meetings in the past fortnight to address matters.
"We've sat down, looked at video clips of what we've won and what he's done right and what we need more of so I think the communication has been very open and consistent.
"It's been the same role we've said from the start and want now so nothing's changed there. I think, Zack needs to accept that's what we need from him."
Flynn feels Atkinson understands what is required but that hasn't translated to efficiency on the court as of late.
"The role has been the same from day one from the first conversation and looking at his numbers from previous years, he's been an outstanding rebounder and a great shot blocker.
"He's a guy who can catch close to the rim and finish at the rim."
However, Flynn is adamant it isn't a witchhunt to make Atkinson a scapegoat for the Hawks' shortcomings.
"I think everyone takes a share in the blame - myself, players - we all do.
"I think it's a very important point that it's not all on one player. No one's deflecting it on anyone."
He reiterates the franchise's biggest issue is the lack of consistency.
"He's just been one of our players who hasn't been consistent. I take the blame as well so I need to help them find that consistency."
Flynn has complete faith in Atkinson and, basing it on his input in the wins, he's under no illusions "Atkinson's best really helps us".
"I really hope we can get him back to that so I still believe in him."
That faith also extends to his entire squad "and they all want to get better so we need to do this right now".
"When we are at our best it's not good enough because we're 20 worse than the next team so consistency is our main thing."