If your ticket starts in the UK, I class is inflexible: no changes, no refunds.

R class (the next most expensive class) has a degree of flexibility. You can change for a change fee of £300 plus any fare difference (particularly if you have to change to a flight that has no R class left and you have to rebook into a higher booking class, like D, C or even J).

Fundamentally, change fee plus fare difference also applies to changing D class or C class fares.

If you buy a J class fare, in certain circumstances you could still be liable for a fare difference if you change even though there would be no change fee. However, this is unlikely if you are only changing the inbound half of a round-trip ticket.

You can actually combine an I class outbound with an R class inbound (or D, C or J class inbounds). That way, you can get the cheapest possible half-round-trip fare outbound (with zero flexibility on that half) with whatever flexibility you require inbound. The fare rules provide that the changeable half remains changeable.

However, as Cymro asks, if your inbound date is fixed and only the time is uncertain, and if you're flying back from JFK, why do you want any flexibility at all and why do you want the flexibility of a J class fare?