Low amniotic fluid at 39 weeks. Should they deliver?

Probably. If your afi is < 5, yes. If it's borderline, between 5-8, it should be strongly considered unless your cervix is unfavorable (difficult to induce d/t being closed, thick, and/or firm). If they wait, you also need a normal non-stress test (nst) or biophysical profile (bpp). If your afi > 8, it's ok to wait. Discuss this with your OB & make sure you understand "kick counts" & when to go to l&d.
Probably. The amniotic fluid does start to decline by 39 weeks, but if the level is below what is normal (usually an afi of 80 or more) then delivery should be considered as there may be no particular benefit to prolonging the pregnancy beyond 39 weeks. The complication rate for delivery will usually increase as the fluid level decreases.