I've just been at my father's and, since he has an Ipad, tried it for myself. Now I know the reason the embedded player does not work for you is mobile Apple devices don't run Adobe Flash player. Some quick googling told me there are alternative browsers which might work, or not; it is a general political issue between the companies or so.

Can you please tell me if the following works for you?
Go to one of the files on Tindeck, for example this one, and click on the "download track" link. Can you get the link and does it work for you?
It worked on my father's Ipad and on my PC.
If it does for you, I'm including a direct link on the entry above.