I could buy Bitcoin from a local exchange site and transfer it directly to trading platform (kraken). So, instead of adding my Desktop's wallet address, I could add kraken's generated BTC address.

Is it safe? Does it have advantages or disadvantages?

P.S: I can buy from kraken, but the fees are high and it's time consuming.

L.E:
Buying at my local exchange it's much more cheaper (if I subtract the fees) and it's faster. Actually the prices are higher, but if I subtract the fees it's cheaper. But as I said, this service is an exchange, not a trading platform like kraken.

In order to buy from kraken, I need to convert my local currency to USD (1.15% fee), transfer to Kraken's bank address ($16 fee) and it can take 2 - 5 business days and after that buying with 0.26% (market price) or 0.16% (limit price). If I buy on local exchange, it takes only 5 - 15 minutes and aprox 1h to receive the bitcoin in my wallet.

I'm asking if it's safe to add kraken's BTC address instead of my local Desktop's wallet address so this way I can save more money instead of just throwing on fees. Is this safe? Can the transaction be lost?