Basically what I am asking is, can I copy and paste an answer I have submitted on another post even when I reference it? Or is it frowned upon? Would you rather a link to the original answer?
I think the best thing to do is:
First figure out if you think the questions are duplicates. If you believe so, flag one of them as a duplicate of the other. As Seth says, this is most often the case.
Typically you will be flagging the question you considered posting an answer on (as the duplicate target should almost always have one or more answers that really do answer the question being closed as a duplicate). This is most often also the more recently posted question.
When are they duplicates, rather than questions that might share an answer? Unless you expect that other valuable answers would apply to one and not the other, and that neither question can reasonably be broadened to account for this, they are probably duplicates.
That is a general guideline or heuristic--not a rule. You'll have to use your judgment, or ask others for their input (you can post on meta, or if you have enough rep to talk on chat, you can discuss it there).
If you do not believe they are duplicates, but you do think your answer on the other question--or someone else's--answers it, write an answer that addresses the differences that made the question not duplicates.
This answer should cite the answer on the other question (whether or not that answer is written by you). Sometimes the best thing to do is restate part of it, and provide a link for more information. Other times, block-quoting from the other answer is the best way. This is for you to decide. You might combine the two.
Unless the other answer is very short, you should probably not quote the whole thing. (Though there is no copyright problem in doing so provided it's rightly credited--both it and your answer will be licensed under CC-BY-SA 3.0).
Instead, what you are doing is to adapt the answer to the different question you are answering, in such a way as to address what is different about it, creating a different answer in the process.