How long does it take for a directive from the Pentagon to reach the appropriate command in order to combat this virus?

Also, as I now realize I didn't answer your question; it should be very rapid, these orders are published on the G 3/5/7 portal, all you need is a CAC and reader to access unclassified orders.

SSG (Join to see) Roger Sgt, I was able to catch up on everything via Facebook right after posting this question. If I am understanding correctly, FRAGO 14 gives power back to the Commanders on how to proceed. 2ID has been HPCON CHARLIE for three weeks now and it's been business as usual. We are still conducting PT, ruck marches, ranges, still forming up for Motorpool Monday, etc, despite the guidance here being to expect cancellation of all in-person gatherings.

SPC (Join to see) - Considering where you are, I am not surprised about the business as usual aspect of what you are seeing. I would hope that you do realize that even though you there are issues with COVID-19 in Korea, that you are still in a Combat Zone. Yes, I know that it does not appear that way and that the 2nd ID is not as near and next to the DMZ as they have been in the past, it is still a Combat Zone. And though you may not see it, I know that the ROKA isn't in a stand-down posture because of COVID-19. I can easily tell you that those units on the DMZ have actually moved up 1 or 2 threat con levels, for them it is business as usual - prepare for combat.
Those in other combat zones may have hunkered down but they are continuing to conduct business as usual just under a tighter leash.

Sir, we still have PT formations and still do PT. We have BN formations for Motorpool Mondays, and training is still being conducted. It's business as usual with the occasional "sanitize your hands."

SPC (Join to see) - How long have you been in Korea? Are you assigned to one of the short rotational units cycling through Korea?
Since you are a Horizontal Construction Engineer, I have a suggestion or two. Use Google Earth or Google Maps and look at the area between you and Munsan-eup. And then get with your immediate leadership and find out (if you do not already know) what your unit's area of operations is expected to be. And then start drilling down to where you can check out some of the detail. If you need assistance in knowing what to look for start with a close examination of the area between Camp Bonifas and Panmunjom and the areas to the west past the rail bridgehead at Dorasan-ri, and then pull out your manuals on fortification construction and demolition.