Flannery, who had been among the original 37-man Lions party to tour South Africa last summer, pleaded guilty prior to being sentenced and acknowledged that the offence deserved a red card at the time but he hopes to have the length of the suspension reduced.
The appeal will be heard on Wednesday of next week in London.
An independent appeal committee, chaired by Judge Jeff Blackett, the disciplinary chief of England's Rugby Football Union and also consisting of Italy's Marco Cordelli and Douglas Hunter of Scotland, will decide Flannery's future.
The Six Nations disciplinary officer has also launched a cross-appeal, meaning that Flannery's ban could be extended if his own appeal fails.
The current length of the ban means Flannery will miss the remainder of Ireland's defence of their Six Nations crown, as well as up to four Magners League games.