Expressions like "maternal uncle" (meaning mother's brother) or "cousin brother" (meaning male cousin), used commonly in e.g. Indian English, define more subtly the relationship between people in question.
But are these used in standard English (British, American)?
From the perspective of a British English speaker I would not use 'cousin brother' but as Alexander mentions in his comment 'male cousin' is used on occasion, where clarity is needed. But most of the time I would just mention my cousin by name.
I have used the phrase 'maternal uncle' myself, but that was when I was discussing medical history with a doctor where knowing which family line I was referring to was important.
Phrases like 'maternal uncle' or 'paternal aunt' are not used in everyday speech by most people. These phrases are rather formal and mostly likely used in specific circumstances such as legal or medical matters.
For an AmE answer, I would never use "cousin brother." If the gender wasn't obvious from context and pronouns, I would add "he's a guy" or something of that nature.
I rarely hear/say "maternal uncle," although that is the best fit. It is usually not important - plus if you say something like "Uncle Bob," like you do when you are a kid, unless you have two uncle Bobs, you're fine. Even then, I have two Aunt Debs, and the family just calls the married-in one by her maiden name.
However, "maternal grandfather" and the like are fairly more common, especially since grandparents are talked about without their name more than aunts and uncles. You only have four grandparents, and they kind of identify you, while your aunts and uncles are extended family. For example, "my paternal grandmother died last year, but my maternal grandmother is still alive," in response to a question such as "do you have any grandparents still alive."
