Yeah, getting SSSS isn’t a big deal for departure security. Just be aware that there’s a chance you’ll also be subjected to a secondary inspection by CBP upon arrival at JFK.

I had SSSS on LHR-BOS last month and was subjected to a secondary customs inspection at BOS upon arrival. I sailed right through immigration without any hassle, though I do have GE. The secondary customs inspection entailed a baggage X-ray and a short conversation with the customs agent about customs declarations (importing foods, contact with livestock, etc). It was a total non-event.

FWIW, I was traveling on BA on a revenue J ticket purchased 4mos in advance, though I don’t think that has any relevance to getting dinged with SSSS.