It is not 当て字 but it is 慣用読み (reading of a word or kanji using its customary pronunciation -which is not necessarily correct-)
The dictionary says the origin is 足んぬ (たんぬ) sound changed to たんのう and then the kanji 堪能 was applied as ateji.
Meant to be a reply to Matt_Zenuka
@Matt_Zenuka: Yeah I guess we're both right. It depends on the meaning. If you read 堪能 as たんのう to mean the same as かんのう "proficient, skillful" then it's just 慣用読み. So my personal theory from the OP regarding etymology is just wrong. But if you use the word to mean "enjoying, satisfaction" then it's really 当て字. Seems like the Japanese shared my overall confusion with these two words and that's how the additional 慣用読み came into being ;)
Origin of this ateji reading
As the dictionary entry points out, 堪能 is actually ateji for the word たんのう. This was a bit surprising to me, as it seems like on first glance that these could be regular readings. The origin however is 足んぬ (たんぬ) so that's where the "being satisfied" meaning comes from. And then probably from that evolved the "being skillful / proficient" meaning.