Welcome to the Wefugees Community and thank you for sharing your question.
I made some research and learned, that so-called Dublin cases are not entitled for the REAG/GARP programme, which is the state financed voluntary return program. Please see the following document for more details (http://files.returningfromgermany.de/files/REAG-GARP%202018%20-%20Infoblatt%20Englisch_Stand%20Januar%202018.pdf).
However, I am not an expert on voluntary return and there might be alternative programs of support. I can recommend you to consult a migration counselling office which is specialized on voluntary return. There is a search engine, which makes it very easy to find an office close to your place of stay. You will find many organisations and institutions (the independent NGOs marked with a green point), which offer their services confidentially and free of charge. More important, they not only advise you on returning to your home country, but also on your perspective and chances in Germany.
I find your case really interesting, as your initial asylum application was filed many years ago. The question, if one can reapply for asylum in another country after having returned to the home country for a while, was discussed earlier on this platform already. You may want to check this thread for more information.
In this context, it might also be helpful for the community to know, what happened with you, after your initial asylum application was rejected. Did you return or stayed in that country?
I hope this helps for now and please feel free to get back to us with any further question and if you want to discuss your case in more detail.
All the best,