How to get static image url from flickr URL?

With specifying extras=url_o you get a link to the original image:

https://api.flickr.com/services/rest/?method=flickr.photos.search&api_key=YOURAPIKEY&format=json&nojsoncallback=1&text=cats&extras=url_o

For downscaled images, you use the following parameters: url_t, url_s, url_q, url_m, url_n, url_z, url_c, url_l

Alternatively, you can construct the URL as described:

http://farm{farm-id}.staticflickr.com/{server-id}/{id}_{secret}.jpg
or
http://farm{farm-id}.staticflickr.com/{server-id}/{id}_{secret}_[mstzb].jpg

In your Flickr URL, the photo ID is 2658147888. You use flickr.photos.getSizes to get the various sizes of the photo available, and pick the url you want from that, depending on the size. There are several ways to access the API so please specify if you want more details for a particular language.