The Manchester-based side will face defending champions Hendon United Sports Club A.
And joint-manager Stuart Delmonte is on a revenge mission at Boundary Park on May 17.
He said: "It’s great that we are still in with the chance in four competitions. But I think Hendon will offer us the biggest test of our ambitions.
"They are a strong team and their record speaks for itself. It will be an evenly matched game.
"Hendon beat us in last season’s quarter-final and that still hurts. That will act as real motivation for us."
Flixton made the long trip down the capital but had this tie wrapped up by the break.
Harmen were missing six key players in top-scorer James Gershfield, Marc Foster, Daniel Green, Mike Pearson, Rob Blackman and Ricky Rinder, with Danny Cohen filling in at right-back at short notice.
Adam Gilman and an own goal had Flixton in command early on.
Leor Sidle struck and Harmen’s faint hopes of a comeback were ended when they had Oli Leslie sent off for a professional foul.
Substitute Michael Warwick’s long-range free-kick added the gloss late on for the Accountant Premier Division champions.
Co-manager Tony Rosenberg added: "Our defence was magnificent and our strikers scored the goals. You can’t ask more than that.
"We looked pretty comfortable and without James Gershfield, their top-scorer, they and lacked a few ideas. We now move on and the games are coming thick and fast.
"But we would rather be challenging for trophies than having nothing to play. It keeps things bubbling over rather than going through the motions at the stage of the season."
Harmen joint-manager Oli Leslie told JC Sport: "To come this far in our first season as a new squad is a tremendous effort, currently third in the league and reaching the semi-finals of the Morrison, but next year we are determined to go further and win both of these competitions and the Anekstein cup.
"With the additions to the squad that we have planned for the summer, we are confident of achieving these goals. The spirit is amazing amongst the boys and we will now kick on and secure third spot in the league."
Co-boss Joel Alterman added: "We are very disappointed with the outcome of the game, especially as all of their goals came from our mistakes. However they capitalised on this and took the chances that they were presented with.
"It’s always difficult having to travel up or down the country for a big fixture like this and I’m sure Stuart and the boys enjoyed their three-hour trip back to Manchester a lot more than we enjoyed our 15-minute journeys home.
"We wish Flixton all the best in the rest of their season. They will face a difficult test in Hendon and it is difficult to pick a winner at this stage. I can see it going to extra-time before the tie is decided."
