I know of no citations in the ORs with regards to Cleburne keeping his flags for the 1864 campaign. The only evidence we have of such a thing happening, besides the existing flags temselves of course, are things like Buck's accounts, etc.
In his memoirs, Buck writes: "At Wartrace, new flags were ordered to be issued, but when the troops of the division learned that their old battle flag - blue and white - was to be replaced by the newly adopted regulation one a hurricane of protests was heard..." (Cleburne & His Command, Page 130).
Buck is in error as to the time frame here. Cleburne's men were posted at Wartrace from January, 1863 through June, 1863, and while new flags were indeed issued at this time, there was no army wide flag standardization at that time. Braxton Bragg never seemed to care what flags his troops carried for they still were carrying a number of patterns in 1863.
What Buck meant to write was that this took place at Dalton, GA in February, 1864 when Joe Johnston ordered new flags for the AOT.
The flags that Cleburne's Division used in the Atlanta Campaign were newly issued and their "moons" were rectilinear. After the campaign, where some flags were captured, new flags were issued in October, 1864. Within this new issue, Mercer's GA Brigade, having joined Clebrune's Division after the battle of Atlanta in July, also received their first Hardee battle flags replacing their flags of the Charleston Depot. All of the flags reverted to the circle as the "moon."
Hope this helps,