There are two schools of thought as to where wild yeast comes from for a sourdough starter. One is that is in the air, the other that it is present in flour.
Having made a few starters myself and trying different methods, I am of the opinion that the latter is more likely. I have had just as much success with starters I have simply mixed and put in a sealed jar as with the ones I have walked around the kitchen, vigorously stirring with my hands and so on.
You can maximise your chances of having plenty of yeast in your flour by buying organic, as there will have been no chemical treatments which might destroy the yeasts, but any decent flour should have more than enough yeast naturally present to make a starter with.
Yeast, however, is just one aspect of sourdough - you are also looking to cultivate various Lactobacillus species which produce lactic and acetic acid, which is what makes sourdough sour. These are everywhere and so there is no problem with finding them.
However, there are also 'bad' bacteria species that can make your starter go bad. To minimise the chances of this bad bacteria multiplying, it's a good idea to lower the pH of your starter, and for this reason I have had much more success with starters that use pineapple juice. Follow the recipe in this blog, replacing the water on days 1 and 2 with normal, unsweetened pineapple juice, and you'll be on your way.
I agree with rumtscho that your dough is probably way too wet, but I'd like to make a few other points as well:
You don't necessarily need to add extra flour just because your dough is sticking to the bottom of your bowl. And definitely don't add any flour until your dough is fairly smooth (unless you already have a feel for the recipe). The flour will absorb a lot of water as you work the dough, so dough that seems way too wet after one minute of kneading may be fine after six.
Also, I've found that with the hook design in the Kitchenaid, dough frequently sticks to the bottom even with proper hydration. Just use a scraper to turn your dough out of your bowl and give it a fold to make sure that there isn't an underworked spot on the bottom.
Best Answer
You can certainly maintain a culture this way, though not all cultures will necessarily thrive. Commercial yeast, for instance, doesn't tend to do well with feedings. It basically rises and it's done. Wild yeasts will do much better by being fed.
The degree of sourness in the cultured flour will depend on the specific strains of yeast and bacteria growing in it. You can control this to a degree by adjusting the hydration level and temperature to encourage specific strains of microorganisms to grow.
Here is a link describing how to control some of the cultures in your starter.