How to apply multiple chroma keys in ffmpeg?
Instead of always using [1:v], you would use the output of the previous one e.g. [ckout1]
My guess, you want this:
ffmpeg -i input1.mp4 -i input2.mp4 -filter_complex '[1:v]colorkey=0x6AA999:0.1:0.2[ckout1];[ckout1]colorkey=0x4D827A:0.1:0.2[ckout2];[0:v][ckout2]overlay[out2]' -map '[out2]' output.mp4

(Maybe the inputs switched around)
The overlay you are using is from https://ffmpeg.org/ffmpeg-filters.html#colorkey? My guess is, that you misunderstood, what the overlay does in the example there. The example describes overlaying 2 opaque videos on top of each other, where the upper video receives transparency first.
What you are doing is overlay the transparent version of input2 onto input1 and then colorkeying input2 again and putting that also on top of input1 and the first colorkey.