"We must produce more cars."
Translation:Vi måste tillverka fler bilar.
They're interchangeable in this case, but not always: only flera can mean 'several'.
fler/flera is the comparative form of the adjective många, so it does not inflect. So flera isn't more plural, but it is more ambiguous – fler bilar can only mean 'more cars', but flera bilar can mean either 'more cars' or 'several cars'.
To begin with, mer is generally used for uncountable nouns, and cars are countable, so the best option might be using fler: But, this distinction isn't absolute. It depends a bit on how you think about the cars. Maybe they're viewed more as 'goods', so that they're not really seen as individual cars, and in that case, mer works too.
As for mer or mera in this case, both are OK but mer is overwhelmingly more common. (I've added mera.)
mer is an adverb, so it does not inflect like adjectives do.