You cannot omit the 'the', because the sentence would be wrong without the article. You have to use 'the' in this sentence because you are talking about specific streets. You are referring to the specific streets of the city in question.

'Seven more people died in Iraq, where people fled into the streets in the capital, Baghdad.' You use 'the' when you are referring to a particular example of that thing, in this case streets in Baghdad. When you remove 'the' from this sentence, then the structure must also change in order to retain the same meaning or else it will sound weird.

the streets

Re-posting my comment as answer.