Künkler is a fellow of the “Women Creating Change” Project on Gender, Religion, and Law in Muslim Societies at Columbia University, New York, NY, and co-PI of the Iran Social Science Data Portal. She is a Senior Consultant to a project on “Islamic Authority in the Middle East” funded by the Luce Foundation, and a fellow of the project “Confronting the Governance Crisis in the MENA” funded by the Carnegie Corporation. She is a member of the International Advisory Board of the Cambridge Journal of Law and Religion, as well as member of the editorial boards of the Journal for the Scientific Study of Religion (Wiley), Perspectives on Religion and Politics (Brill), and the International Journal of Islam in Asia (Brill). She is a Member of the MESA Committee on Academic Freedom, deputy chair of the Scientific Advisory Council for the Centre for Global Cooperation Research, University of Duisburg, and a former Member of the Board of the Association for the Study of Persianate Societies (ASPS).
While at Columbia and Princeton universities, Künkler has been a visiting scholar at the Faculty of Social Science, University of Tehran, Iran; the Centre for Strategic and International Studies, Jakarta; the Islamic State University (UIN), Alauddin Makassar (Sulawesi), Indonesia; the International Institute for the Sociology of Law (IISJ), Spain; the Graduate School of Muslim Cultures and Societies at the Free University in Berlin; the Wissenschaftszentrum Berlin (WZB); the Politics Department at the University of Oxford; the Center for Interdisciplinary Research (ZIF) in Bielefeld where she was a PI for a six-month research group on Constitutionalism and Religion; and the Royal Netherlands Institute of Southeast Asian and Caribbean Studies (Koninklijk Instituut voor Taal-, Land- en Volkenkunde, KITLV).