Learn Dutch: Ik kleur de bloem geel. - I am colouring the flower yellow.

In Dutch, the simple present tense (like Ik kleur) often translates to the English '-ing' form. You could say Ik ben de bloem geel aan het kleuren, but using the simple present is very natural and perfectly fine for actions happening right now.

Is kleur a verb or a noun in this sentence?

It is a verb! The verb kleuren means 'to colour'. The noun for 'colour' is also kleur (as in de kleur), but you can tell it is the verb here because it comes right after the subject Ik.

Why is geel at the very end of the sentence instead of next to the flower?

Because it describes the result of your action, not a flower that is already yellow. You are making the flower yellow. If you were talking about a flower that was already yellow, the adjective would go before the noun: Ik kleur de gele bloem (I am colouring the yellow flower).

Why is it geel and not gele?

Adjectives only get an extra -e when they are placed directly in front of the noun they describe. Because geel is separated from bloem and placed at the end of the sentence, it keeps its basic dictionary form.