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I'm not sure what you are referrring to as the Vodafone Starter Kit. I am guessing that you referring to either the SIM Only or PAYG Internet only plans which you will find here. You will be able to use your device in Europe, although please be aware that it is quite pricey to do so, more about the prices here
I'm not 100% sure what they are trying to sell you. I am guessing it may be a PAYG Internet only line. It could be a WiFi device. I would advise that you check with the store you are purchasing the Kindle from.
Vodafone Starter kit appears to be a product sold by VF australia so being as we are on the UK site are we talking about VF australia or VF UK
Anyway to work with a kindle fire you will need a mobile handset or wi-fi dongle capable of outputting an infrastructure mode signal, as the fire cannot see ad hoc wi fi networks
look for a dongle or handset capable of teathering several devices at once
To use your iphone as a hotspot, you obviously need to be using two devices at once instead of one. However, if you don't mind that, it'll be a lot cheaper than paying the extra for a 3G Kindle and a data connection.