You can trade almost most of the exchange without KYC, it's needed only for trading big amount. I have been trading in several exchanges without KYC and faced no problem till date.
However you can't trade on bittrex if you didn't do KYC. You will have 0 btc withdraw limit if you don't do KYC on there
Perhaps, he should try to buy bitcoin on binance because, in that site, he can buy bitcoin without doing KYC. But the best solution to buy bitcoin without KYC is from local sellers in his city so he can avoid the KYC verification because he knows each other. He can trade in binance also without doing KYC, but he got a limit for withdrawing in daily.
I think it will better if he can do KYC in a trusted exchange like bittrex, poloniex or binance because that will help him to increase his withdrawal amount.