360 flex plate

What year of a 340 are we talking about?
Some were internally balanced, and some were externally balanced.
Early ones were forged cranks and internally balanced and later ones ('mid '72 and all '73s) were externally balanced.
I would find out for sure about the one you have and go from there.
BTW, i have seen engines with the cranks swapped in an earlier or later casting date engine, so looking at the block casting date is not 100% accurate.
When you know for sure, give B&M a call and go with their recommendation.
JMHO.