With some surprise I noticed, that if I have such chart(s), then I don't remember about it.
Best I can offer is the chart for 1943 from "The Soviet Air Force Since 1918" by John Boyd (1977).
And I guess that You're not capable of using Russian language, as otherwise You'd look in that language yourself.
Few notes: to begin with, you shouldn't think about VVS (or any other Soviet armed service, for that matter) in the same way you'd think about US armed services, that are completely separate and historically didn't even liked to talk to each other too much (and until 1947 were under completely separate government departments). Soviet armed forces were (and Russian are) an integrated organization, including navy (although this service slightly less than the other ones, and at times there was a separate navy people's commissariat/ministry - but in Soviet practice it meant much less than it would in US practice). For that reason, position of the VVS in the organizational structure of soviet armed forces was slightly more like of the war-time USAAF than the post-1947 USAF.
In 1940, for example, VVS command was one of 19 central institutions of People's Commissariat of Defence (and one of 6 of institutions with status of Main Administration - Glavnoye Upravlyene).
Operational assets of the air force were either under central control (like Long Range Aviation, or other units that could be designated to be under such control) or were controlled by military districts (fleets) - be it as their "own" units, or as part of air defences (under Administration of Air Defence of the People's Commissariat).
Note, that military districts and fleets in Soviet practice are combined-arms commands, a little bit like current US Unified Combatant Commands (albeit on smaller geographical scale).
Also, routine administrative/supply/etc. matters of centrally-controlled air assets would usually also be done via military district in which they were stationed, unless specified otherwise.
In the beginning of the war, each Military District HQ had an aviation command as part of its organization, and individual field armies (level below M.D.) also had their aviation commands. This structure, which was largely reminiscent of practice common in most countries during World War 1 was found to have shortcomings after Winter War and was dropped after disasters of early months of Soviet-German War. In turn, there were no longer aviation commands of M.D.'s (Fronts in wartime), but Air Armies were formed. They were subordinated to front commanders (or were part of GHQ reserve), but weren't further split between individual armies of the front and the Air Army commands were no longer part of the front HQ itself, but they could be moved from subordination of one front to another.