What crypto coin could I best use to transfer my funds from Kraken to Binance?
And is there a general answer for this question? Or does it depend on the Exchanges I use?
It depends on the exchanges you use. You need to find a coin that is supported on both exchanges and then check the withdrawal fees to find the cheapest.
Or can this change on a daily basis (due to network fees)?
Although most exchanges don't change the withdrawal fee (use dynamic fees) the cheapest one could well change as exchange rates constantly move. For example, someone already suggested DOGE as it always has low fees. But it is also true that DOGE increased a lot in value recently so you need to check frequently to make sure you are still using the cheapest coin.