You can write bilingual captions in the exif data, but the text in both languages should be written in the same caption field.

If you want to have two exif fields with one caption each you could use another exif field for that purpose since you can not just add a "caption2" field to the exif data out of nowhere.

Same thing for flickr: You can add text in any language you want to the photo description, but all the text will be on the same photo description no matter what language you are writing in.

I tried to do something like this last year and writing everything into a single caption field and description was the less painful way to go. If you REALLY want to go for it no matter what, the best solution I can think of is to misuse one exif field for the alternate caption and then create or find a script that joins those two captions and dumps them into the flickr photo description.