Why would you transfer them from one trading platform to another in the first place? The only advantage I see is not having to pay more fees, instead of sending them to your desktop wallet then sending them again to KRAKEN, you can send them directly and not having to pay the network fees that your wallet will calculate, its nothing much anyway.
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?
It is completely safe to send Bitcoin on your Karken Bitcoin address. This is how the trading is done. We all send bitcoin to exchanges for buying altcoins. Buying at local exchanges also give arbitrage opportunity.