1. The reason that I'm a 266 on chesskid.com is because I've only played 4 slow games, all of which were against you.
2. You can't really use your chess.com rapid rating of 1566 as evidence, since you've only played a few games on that time setting.
3. The same goes for my chess.com rapid rating of 1105--I haven't played enough games for that number to really mean anything.
4. All the ratings that you mentioned were below 1700. There are quite a few players on chess.com with ratings much higher than that, so the range of your data is limited.
5. Don't forget that on chesskid.com, most of the people playing are, well, kids.
I joined chess.com 24 days ago and before I was playing on chesskid.com (as the username ObservantComet) . I noticed that all the ratings of me and my friends were lower in chesskid.com than in chess.com. I have ocassionally played on chesskid.com even after I have started to play on chess.com so it can't be that I got better when I joined chess.com. Here is the data I collected of my friends and my ratings on chess.com and chesskid.com:
My chesskid fast chess (15min rapid) rating: 1090
My chesskid slow chess rating: 1202
My chess.com rapid rating: 1566
My chess.com slow chess (daily) rating: 1298
My brother's (his username is BoundlessCity on chesskid.com) chesskid fast chess rating : 681
My brother's chesskid slow chess rating: 266 (I know lol and he is older than me)
My brother's (AmbroseWinters on chess.com) chess.com rapid rating: 1105
My brother's chess.com daily rating: 1203
One of my friend's (koko on chesskid.com) chesskid fast chess rating: 1283
My koko's chesskid slow chess rating: 1599
My friend's (Kokolam on chess.com) chess.com rapid rating: 1643
Kokolam's chess.com daily rating: 1550
It seems to me from the data, as well as games that I have played on both sites, that chesskid.com ratings are deflated or chess.com ratings are inflated (less likely). If you have a chesskid.com account post your ratings on both chesskid.com and chess.com. Thanks!