I would think there was a structure more so for frequencies rather than command. The army had many layers of wireless comms from front line back to hq. Air force comms were mostly two modes, air to air (VHF?) and laisson (HF?).
There was no middle man from takeoff to landing except in ground support.
The mobile ASSU (army) would provide targeting info directly to the pilots. For D-Day Combined Ops introduced the fighter direction tender. These were LSTs converted to floating radio & radar stations to support the RAF & the RCAF. There was probably a nice bit of kit on these. I read that they were equiped with German radar sets due to the thought that Jerry would jam British sets but not their own
As airfields were acquired I suspect comms were more telephone and RTTY.