How do you sample a GPIO input port (LED)?

Instead of sampling it, you could capture the rising (or falling) edge with a Timer. Capture channel.

You say P2.3 (I guess layout is already done?)

Good thing is that pin can be TA1.0 (most likely but as we don't know what msp you have)
So setup timer A1 continues-up in CAP mode.

create a IRQ for it so when it have been triggered, you read the ccr0 value
No need to hurry to the IRQ as the value have been captured and is there waiting for you.

Store it and when next capture happen, subtract the first value from this new value = length between pulses.
If you use 16bit unsigned values, counter overflow between the two pulses is no problem.

Sorry, it's actually P2.4 input.  It is a MSP430 F5310 series.  it is a TA2.1 CCR1 capture: CCI1A input, compare: Out1 output

That's the spec for MSP430F5310.  So I just use an interrupt timer to capture it and compare the clocks?

Okay, I guess I"ll need to study up on how to write timer interrupts.  

It is quite "nature" to use interrupt, and it is "good for you" to study how to use that.

But pulling the IFG without interrupt is okay too -- if the CPU is not busy doing other things.