Learn Turkish: Arkadaşıma bir çiçek hediye ettim. - I gave my friend a flower as a present.

Arkadaşıma is made of arkadaş (friend), -ım (my), and -a (to). The compound verb hediye etmek (to give as a gift) requires the dative case (-a or -e) to show who is receiving the gift. Literally, you are saying 'to my friend'.

Why do we use ettim after hediye?

Hediye is a noun meaning 'gift' or 'present'. In Turkish, we often create actions by pairing a noun with a helper verb like etmek (to do/make). Together, hediye etmek means 'to give as a gift'. Ettim is simply etmek in the past tense for 'I'.

Should çiçek have an accusative case ending since it is the object being given?

No, because it is an indefinite object ('a flower', not 'the flower'). Turkish only uses the accusative case for specific, definite objects. Because we use bir (a), çiçek stays in its plain dictionary form.

Could I say 'Bir çiçek arkadaşıma hediye ettim'?

You can, but it changes the natural focus of the sentence. In Turkish, the most important or newest information usually goes right before the verb. By putting bir çiçek right before hediye ettim, you emphasize that you gave a flower, rather than emphasizing who you gave it to.