Then shouldn't the translation be "I don't like the chairs"?
"I do not like the chairs." (the "best" translation, at the top of this page) and "I don't like the chairs" are the same, and both should be accepted if they are not already.
Is Szeretem an definite conjugation..
Yes, szeretem is definite. It's required here because the object is a székeket, the chairs, with a definite article.
How would one say "I don't want the chairs."?
Nem akarom a székeket.
You can also say "Nem kerem a székeket." The suggestion above is also valid, but you sound impolite, like a child.