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I don't think you can tell the date the photo was taken from the data you have presented by itself.
But at least you could find out a 'latest possible time' limit for the photo, by comparing the numbers in its URL with those in Flickr photos you *do* know, or can determine, the date for. The numbers in the URL may be directly related to 'order of posting' among all photos on the site Flickr.com, so finding a photo with a URL number before, and one with a URL number after, the one you have cited, with dates you can be sure of, would 'bracket' the possible time of ... posting on Flickr, if not the time the photo was taken. But that would at least be a 'latest possible date/time' for the photo's being taken.
Flickr does have recommendations as to file dates - the 'taken' date and the 'posted' date - as mentioned here:
But unfortunately both those dates can be altered (at least by the owner of the account through which the file was posted) as discussed here:
So, realistically speaking, the only way to prove a file-posting date, is to request it from Flickr - or subpoena it from Flickr, perhaps. I'm sorry to have to say it, but for purposes of proving a point at law, that may be the only applicable course.