Learn Italian: Compro un chilo di farina.

In Italian, the ending of the verb usually tells you who is doing the action. Since compro ends in -o, it already means I buy. You only need to add io if you really want to emphasize that you are the one buying it.

Does compro mean I buy or I am buying?

It can mean both! Italian uses the simple present tense (compro) for general habits (I buy flour every week) and for actions happening right now (I am buying flour).

Why is it di farina and not della farina?

When you state a specific quantity like un chilo (a kilo) or un litro (a liter), you just use the preposition di (of) without an article. You would only use della if you were talking about an unspecific amount, like saying I buy some flour (compro della farina).

Why is it spelled chilo instead of kilo?

The Italian alphabet traditionally does not use the letter k. To get the hard k sound before an i, Italian uses the combination ch. If it were just spelled c-i-l-o, it would be pronounced chee-lo, so the h is needed to make the kee-lo sound.