I am not 100 % sure how you have done this, but here's my tip.
Don't use the resource itself to output the JSON. Doing this based on a GET-paramter will required the entire site to be uncached. Instead, use a single resource for the feed and supply the id/permalink there.
For example: mysite.com/feed?id=1
, mysite.com/feed?latest
or something like that.
Done this way, you could have an empty template with just the snippet that is parsing to JSON in it. This has to be uncached of course, but the rest of the site could be cached as normal.