I haven't tried on this particular platform, but you should be able to access a standard boot flash via OpenOCD and any supported third party adapter, there are various config files for MPSoC platforms.
There are two methods, one is the CPU built-in in circuit emulation which works for standard boot flashes, typically. The hard low level method is boundary scan which allows you to selectively toggle pins, but you need a config file and be very much aware of which pins you are toggling, meaning, there is no general solution and you might have to dig into the BSCAN tools.
WRT original JLink, I remember issues with different firmware versions in openOCD, but in general it should work.