Upvote:2
You could fly to Frankfurt and take Condor 2162 to Montego Bay (MBJ). Edit: you can find tons of flights from Montego Bay to Europe here. As you can see flying to Kingston has much less options.
The best avoid-EU option is to take SU150 to Havana, Cuba and then Blue Panorama Airlines BV 1302 to Montego Bay. This is only on Wednesdays and it's not clear whether you can buy a ticket for this section only. The flight exists but the Blue Panorama website doesn't offer a ticket. A phone call to Blue Panorama is in order. Otherwise, take KG6081 to Montego Bay (via Holguin, Cuba) also on Wednesdays only but you need to fly on Tuesday to get there on time. Russian citizens do not need a visa to Cuba (noone should be surprised) which makes this option superb alluring if you don't want to mess with visas. If the BV1302 section is available this also must be the fastest option.
Or connect via Panama to Kingston (no visa needed either) or Grand Cayman to Montego Bay (I do not know the visa situation for this option).
Another long way around the EU is to fly to Dubai take Emirates to Panama City (longest commercial flight in the world) and Copa to Kingston.
Upvote:4
Just avoid any US-based airline; and you will not have any stops in the US. Your Aeroflot flight was a codeshare with American, which is why it had a stop in JFK.
You might also want to avoid any code-share flights with Canadian airlines; since Canada does not offer TWOV (transit without visa) for Russian citizens.
You can fly British Airways (assuming your girlfriend can transit through the UK) and take BA2263, a direct flight from Gatwick to Kingston.
You can also take KLM757 from Amsterdam to Panama, then COPA418 to Kingston.
Just avoid any US or Canadian flagged airlines and you should be okay.
You can use tools like Google flight search to see what airlines fly the routes. The link takes you to a search for flights departing all airports in Moscow to both Montego Bay (MBJ) and Kingston (KIN).