There isn't. All cases use 'vlees'. Is there a plural for meat in other languages? I've never used the word 'meats' either. If you want to say you have different kinds of meat, you say 'verschillende soorten vlees'. Or 'two pieces of meat' are 'twee stukken vlees'.
Portuguese has plural for meat as well as many other languages. It is used when you need to reffer to different types of meat, or an assortment of "cold meats"
It's a bit like the th in thought. It's closer to the f in fear, but a little bit softer.
As Susande said - it's definitely a 'v' sound, but aspirated a little so it's not a really hard v.