kamo ga tubasa wo habatakasete, tobitatta.

It is read:

• 鴨 = かも
• が = が
• 翼 = つばさ
• を = を (pronounced o)
• 羽ばたかせて = はばたかせて
• 飛び立った = とびたった

So the full reading is:

かも が つばさ を はばたかせて、とびたった。

It breaks down like this:

• 鴨が = the duck
  • subject marker
• 翼を羽ばたかせて = flapping/making its wings flap
• 飛び立った = took off

So the structure is:

[subject] + [first action in て-form] + [main action in past tense]

The main verb comes at the end, which is normal in Japanese.

が marks 鴨 as the grammatical subject of the sentence.

In a sentence describing a specific event, が is very natural:

• 鴨が...飛び立った = The duck took off

If you used は, it would make 鴨 the topic instead:

• 鴨は...飛び立った

That is not impossible, but it gives a slightly different feel, such as talking about the duck as an already established topic, or contrasting it with something else. が is a straightforward choice for a simple narrative description.

Japanese often leaves out possessive words like my, your, or its when the owner is obvious from context.

So:

• 翼を羽ばたかせて literally says flapping the wings
• but naturally means flapping its wings

This is very common with body parts:

• 顔を洗う = wash one's face
• 手を上げる = raise one's hand
• 目を閉じる = close one's eyes

Since the duck is the subject, it is obvious that the wings are the duck's wings.

翼（つばさ） means wing as a body part.

羽（はね） more basically means feather, though in some contexts it can also refer to a wing. It is also used as the counter for birds and rabbits.

So in this sentence, 翼 is the clearest word for wings. It sounds descriptive and fits well in written narration.

Yes. 羽ばたかせて is the て-form of 羽ばたかせる.

Related forms:

• 羽ばたく = to flap (one's wings)
• 羽ばたかせる = to make something flap / to cause wings to flap

So:

• 翼を羽ばたかせて literally means something like causing its wings to flap
• in natural English, that becomes flapping its wings

This kind of causative is common when someone deliberately moves a body part or causes something attached to them to move. It does not necessarily sound like forcing in the English sense.

Yes, that would also be natural.

• 鴨が羽ばたいて、飛び立った。 = The duck flapped its wings and took off.

The difference is:

• 羽ばたいて uses 羽ばたく, which works by itself
• 翼を羽ばたかせて explicitly mentions the wings

What you normally would not say is:

• 翼を羽ばたいて

That sounds wrong because 羽ばたく is not normally used with a direct object marked by を. If you want to mention 翼 explicitly as the thing being moved, 羽ばたかせる is the natural choice.

The て-form connects actions.

Here, 羽ばたかせて links the first action to the second:

• 翼を羽ばたかせて = flapping its wings
• 飛び立った = took off

So the sentence means that the duck flapped its wings and then took off, or took off while flapping its wings.

The て-form can show:

• sequence
• accompanying action
• manner

In this sentence, sequence and manner are both reasonable.

飛び立った is the past form of 飛び立つ.

• 飛ぶ = to fly
• 飛び立つ = to take off / fly off / launch into the air

So:

• 飛んだ = flew
• 飛び立った = took off

飛び立った focuses on the moment of leaving the ground, water, perch, or other starting point. That makes it a very good choice here.

Japanese nouns usually do not show singular vs. plural the way English nouns do.

So 翼 can mean:

• a wing
• wings

The context tells you which is intended. Since a duck normally uses both wings to take off, English naturally translates it as wings.

No. In ordinary Japanese, this sentence would usually be written without spaces:

鴨が翼を羽ばたかせて、飛び立った。

The spaces are just a learning aid to make the parts easier to see. Japanese normally does not separate words with spaces the way English does.