"I am available" = "я доступний"
but if someone wants to see anyone or what else then speak in general cases:
English "I am available ...."
українська: "я вільний ...."
Thank you. I am fluent in both Ukrainian and English, but I see the connection between "I am free" and " I am available" as only applicable in two of the wide range of their meanings/applications. One of the two meanings is the one you mentioned. As so, I do not think they are interchangeable and disagree with Duo's representatives using "I am available" where "I am free" indeed should be the right translation.