wrote

Our kitchen sink pipes broke. The pipes are fixable; however, I have
no idea what's happening between the bottom of the sink and the floor.

Like the others said, if it was a short leak now fixed, relax.

I'm not a carpenter and would prefer not to hire someone to remove the
sink floor for $$ sake. Is there something I can spray/pipe between
the cracks into the under the sink and floor? Is there some anti

Yes, a 50/50 bleach and water. Dont go crazy with it, but if it's dry down
there already, a little on top will be just a preventive.

mildew foam or spray with a long plastick hose to fit in hard to reach
areas that could be used?

You dont want to pump much in there at all. Literally at most, about 1/8
cup of the mix for most sink sized areas and even that is a fairly heavy
application.

Unless you have a special family health issue that makes mold a severe
problem (AIDS family or friends who visit, those with serious respiratory
ailments with also imunodeficiency problems etc) then just be at ease. A
short leak fixed quickly before the wood rotted out, is not apt to be a mold
issue.