1. Hwajeon is made from rice cake and flowers such as roses and azaleas.

2. Hwajeon is made from rice cake and flowers such as roses or azaleas.

(Which one is right? Do we have to use 'and' or 'or'?)

That depends upon whether Hwajeon uses only one type of flower -- or more than one.

If only one kind is used, then the second sentence is correct.