Can you also say "vi behöver mer stolar"? If so, what is the difference between the two?
You can, but it’s not as accepted. It’s sort of the same as the ”10 items or less/fewer” thing in English. Stick to ”fler” but be aware of that some people will use ”mer” in its place. In formal language you use ”fler” with things you can count (e.g. chairs) and ”mer” with uncountable things like money or milk.
Coins or units of currency are countable, but money as a general concept is not. Just like you could count drops of water, but water itself is an uncountable noun.
Flera means several, I guess words like fler and mer don't follow the noun it is followed by :)
So "Vi behöver flera stolar" = "We need several chairs", while "Vi behöver fler stolar" = "We need more chairs", right?