Je öfter ich laut lese, desto flüssiger spreche ich im Kurs.

It is the German way to express a correlative comparison:

• Je öfter ich laut lese, desto flüssiger spreche ich im Kurs.
• English: The more often I read aloud, the more fluently I speak in class.

So:

• je + comparative = the more / the less ...
• desto + comparative = the more / the less ...

This structure shows a relationship: when one thing increases or changes, another thing changes too.

Both are comparative forms.

• oft → öfter = more often
• flüssig → flüssiger = more fluent / more fluently

In this sentence:

• je öfter = the more often
• desto flüssiger = the more fluently

German often uses the comparative in exactly this kind of sentence.

Because after je in this pattern, German normally uses a comparative, not the basic form.

So you say:

• je öfter = the more often

not:

• je oft

The same applies in the second half:

• desto flüssiger not
• desto flüssig

Because the je-clause behaves like a subordinate clause, and in German subordinate clauses, the conjugated verb usually goes to the end.

So:

• Je öfter ich laut lese

has this order:

• Je öfter = introductory comparative phrase
• ich = subject
• laut = adverb
• lese = verb at the end

This verb-final order is normal in this structure.

Because the second part is a main clause, so it follows normal main-clause word order rules.

In German main clauses, the conjugated verb must be in second position. Here, the first position is taken by desto flüssiger, so the verb comes next:

• Desto flüssiger = position 1
• spreche = position 2
• ich = then the subject

This is the same kind of inversion you see in sentences like:

• Heute gehe ich nach Hause.
• Im Kurs spreche ich viel.

So desto flüssiger spreche ich is correct.

Because je is closely tied to the comparative expression that follows it.

So German naturally says:

• je öfter ich ...

not:

• je ich öfter ...

You can think of je öfter as one unit meaning the more often. After that, the rest of the clause continues, with the verb at the end.

Because here flüssiger is being used adverbially, not as an adjective before a noun.

It describes how the person speaks:

• flüssiger sprechen = to speak more fluently

Compare:

• ein flüssiger Text = an adjective before a noun, so it takes an ending
• Ich spreche flüssig. = adverbial use, no adjective ending
• Ich spreche flüssiger. = comparative adverbial use, still no ending

So in this sentence, no ending is needed.

Laut lesen means to read aloud.

That is the normal meaning here. It does not usually mean simply to read loudly in a strange or excessive way.

So:

• Ich lese laut. = I am reading aloud.

This is a very common expression in German.

Im Kurs is short for in dem Kurs, meaning:

• in class
• in the course
• during the class/course, depending on context

In this sentence, the most natural English idea is probably in class.

So the speaker means that reading aloud more often helps them speak more fluently when they are participating in the class.

Yes. The comma is required:

• Je öfter ich laut lese, desto flüssiger spreche ich im Kurs.

The sentence has two linked clauses, and German punctuation normally separates them with a comma in this structure.

Yes. In many cases, desto and umso are both possible in this pattern.

So you could also say:

• Je öfter ich laut lese, umso flüssiger spreche ich im Kurs.

Both are correct. Desto is very common in textbooks and formal explanations, while umso is also widely used in everyday German.

Yes, but the meaning changes slightly.

• Je öfter ich laut lese = The more often I read aloud
  This focuses on frequency.

• Je mehr ich laut lese = The more I read aloud
  This focuses more on amount or extent.

In your sentence, öfter is the best choice if the idea is repeated practice over time.

Yes, it is natural and idiomatic.

It is a very standard kind of sentence in German:

• Je + comparative ..., desto + comparative ...

And the vocabulary is also natural:

• laut lesen = read aloud
• flüssig sprechen = speak fluently
• im Kurs = in class / in the course

So this is a good model sentence to learn from.