The 44th got their ANV once they got to Virginia. This has to do with how the Confederate QM operated and that depended on where units were at the time and what departments they were serving under as that department would have been in charge of all QM (and other) needs.
When Longstreet's Corps was in Georgia they were serviced by the Atlanta QM Depot (as well as ordnance). They remained under this depots services until after the Knoxville battle, whereupon Longstreet moved east of Knoxville thus cutting himself off from the Atlanta Depot. They wintered in East Tennessee.
Once there, they came under the supply auspices of the Dept. of SW Virginia thanks to the rail line that ran through Abingdon and on up to the depot at Staunton, which would supply Early's army in 1864. Staunton did make ANV style flags but they looked a bit different than the Richmond Depot flags.
It was not until Longstreet's Corps got back into the Dept. of Northern Virginia that they came back into the supply auspices of the Richmond Depot.
It is evident by the loss of two Hardee flags at Petersburg from the Tennessee regiments (17/23rd and 25th/44th) that they were not issued with ANV flags at the time and did not get them until they lost these flags. Then they would have been issued ANV flags via requisition of the regimental QM by Special Requisition Voucher #40. So they did not get these ANV flags until sometime in the Summer of 1864.
It was not a foregone conclusion that the Tennessee troops that Longstreet "borrowed" for the East Tennessee Campaign were going to go on to Virginia with his corps. The idea was to send them back once Knoxville was captured. After moving east of that city, however, Longstreet was cut-off from the Chattanooga area (thanks to that move and the fighting around the city in late November, 1863) so the Tennessee regiments were basically trapped from going home. They had no choice but to go east with Longstreet after this and they took their Hardee flags with them.