For K-1, your case will go to NVC after NOA2. There is no way to track it. It can take a week to a couple of months for NVC to receive it. Mine took 2.5 months to get there. Others, with the same NOA2, got there in a week. Once it is at NVC, they will assign an MNL case number and forward it to Manila. That will happen 1-3 weeks after NVC officially receives it. You are looking at 1-3 months total for NVC to receive it, assign the case number and send it to Manila. You should request your case status from NVC using the public inquiry form (online) starting a couple of weeks after NOA2 and weekly thereafter until they give you the case number. You can Google NVC public inquiry form to find it.
Once you have the case number, you are in charge of the rest of the process. Do not wait for the Manila embassy to prompt or guide you. They will not. With the case number, you can fill out and pay for your DS-160, then schedule your interview, then schedule your medical appointment once you know your interview date. After all that is complete, you will schedule CFO, which will be the last thing needed before departure.
The time between Manila receiving your case and completion is mostly dependent on how quickly YOU move through the process. Expect some delay to get an embassy appointment, but nothing extreme. It should be no problem to complete everything in the Philippines in 1.5 to 2 months. That's allowing 1 month to get an interview appointment, a week to get passport back, and a week to complete CFO. A lot of it depends on how far away your fiancée is from Manila. If she's close, you can complete things pretty quickly. If she has to travel a lot to get there, that adds time because you have to leave extra time to arrange travel.
My guesstimate would be 3-4 months from NOA2 until ready for departure. There are always variables. It could be quicker or take longer.