1- Everyone should have a right to education.
2- Everyone should have the right to education.
I agree with Ahmed that both are correct and would like to add that, for practical purposes, both sentences mean the same thing: Everyone is entitled to have an education. The use of "the" may be indicative of the fact that the right in question is well-known, having been, for example, established by law. "The right to education" could then refer to "the right to education as enshrined in the constitution."