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Unless I am missing something or that is the wrong link, the antenna is for 144 and 450 MHz. The KiwiSDR only receives to 30 MHz. Unless you have a pretty big discone, it won't work very well at HF.
As to the amplifier, the gain isn't so much a factor as how much power it can put out. If you have no transmitters nearby it shouldn't be a problem. If you do, what ever couples from it's antenna into the receive antenna will be amplified. The amplifier you have the link for says max output is +10 dBm. That is a pretty big signal for a receiver but I don't believe it will harm the Kiwi.