It is possible to convert the same address from Polkadot to Kusama (and thus use the same private key on both networks). You can find a conversion tool here. However, this is not recommended as it can get confusing, and it can cause trouble especially when you use a Ledger. 

We therefore highly recommend restricting each of your accounts to just one network. To do this, find the relevant account on your accounts page, click on the three dots next to it, and then enable "only this network".

If you are managing your account with the browser extension, you can select the right chain in there by clicking on the settings wheel and then "Display address format for"

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