Ah ok, I see the problem.
I need to explain you a bit of how iPhone OS handle audio i/o, so you can understand the problem.
The third party apps, so all the apps on the App Store, have no control over the audio route (headphone/speaker/line-out and mic/line-in) that is used. The OS makes the choice, with the approximate rule "last plugged is used". That means that if you plug headphones on your devices, I have no way to force the OS to use the internal speaker instead.
The problem with this sort of tiny mics is that they will be considered as an headphone+microphone by iPhone OS, despite the fact that they have no jack output ! I even think that as soon as you plug something into the jack input of an iDevice, it will assume that's at least headphones, and will test if it has an optionnal mic input.
What this means in our case, considering the audio route rule I described above, is that it's impossible to output to speakers once you've plugged something in the jack input.
This sort of mic is mostly intended for recording memo for which you don't need simultaneous input and output.
So with this sort of mic, there is no solution to make input + output to work simultaneously. What you can do as a test is recording your audio with the mic plugged, then unplugging the mic and tap the screen with 2 fingers for returning in play mode. That should work, but it's totally useless for a looper.
So I'm sorry

...
But I can recommend you another cheap mic :
http://www.p4c.philips.com/cgi-bin/dcbint/cpindex.pl?ctn=SHH1610/27&slg=en&scy=US . I think it's around 10$/€. That's the one I use for the YouTube video. It's highly better than this more famous and more expensive one :
http://www.monstercable.com/productdisplay.asp?pin=4571 .
Edit : Didn't see the price was in £, so obviously you live in the UK (we are almost on the same time zone, more handy for support ^^). You can buy one on the philips UK store here :
http://shop.philips.co.uk/store/rpeeub2c/en_GB/DisplayProductDetailsPage/productID.165143300