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So the average level of all Pokemon used by Gym leaders in Kanto, Johto, Hoenn, Sinnoh, Unova and Kalos.

I was about to say you forgot Alola, but then I remembered gyms weren't in those games... lol xD
Well even if I had it would have only have been the 4 kahunas
Do you mean individually by region, or every region combined?

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Done! All levels are rounded to the nearest whole. Johto is weird.

Kanto: Lv. 36
Johto: Lv. 26
Hoenn: Lv. 30
Sinnoh: Lv. 32
Unova: Lv. 30
Kalos: Lv. 36

I have the data so if anyone else has questions ya'll can ask.

Hope I helped. :)
Source: PokemonDB

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Since I had the data I also found the averages for what the average level of each gym leader position was.
1st: Lv. 12
2nd: Lv. 18 (okay but there are 34 Pokemon who belong to 2nd Gym Leaders and all of their levels added up to 612. THAT DIVIDES TO MAKE A PERFECT 18 WITH NO DECIMALS OMG.
3rd: Lv. 23
4th: Lv. 27
5th: Lv. 34
6th: Lv. 36
7th: Lv. 40
8th: Lv. 45