I thought I would share some info on soldering here. I dug some old zinc coated tin out of a corner of the shop for the demonstration. The joint is 3/4" deep and I cleated the pieces of metal together. Excess cleat material shows up about every 8" as a dissimilar metal. It won't be there on a roof.

These pieces are for illustration only. They are NOT pre-tinned like they will be on actual roof panels.

Before I start soldering, I preheat the joint.

Adding flux only.

Here, the metal is starting tinning with only a bit of flux.

Added Solder.

Notice the Iron is well away from the edge of the metal, and towards the 'rear' of the seam.

Sometimes, the Iron quits drawing, so you add flux right into the solder.

Now, notice I've drawn the iron along the seam. This pulls solder with the iron. You have to keep feeding solder into the joint where the iron had been, NOT where it is. Keep iron away from edge of joint.

To smooth joint and to clean any trash or dust that floats up, us a clean rag, or even a paper towel. I prefer the reusable 'shop towels' similar to paper towels.

For comparison, I also soldered together a couple of loose pieces of copper. The process is the same.

To start, I pre-heated the copper.

The copper is starting to draw the 'tin' from the iron here. I've added some flux.

Now, I'm starting to add solder. Notice the iron is away from the seam edge.

Iron hasn't moved, and the picture doesn't do it justice, but I'm still feeding solder in the same spot. It's starting to show up to the left of the bar.

 Moved the bar to check solder. It's filling the joint nicely.

Moved the iron, and re-applied solder back where I started. I don't want to draw the solder from the beginning of the joint. So, I keep feeding almost 2" from where the iron is. And yes, the bar is still melting in this picture!

. Doesn't appear to be enough.

So I added more solder. Joint is still drawing,

Finished joint. Note the solder all the way to the left.

End view of the piece. Though there is a holiday at rear of joint in place where iron never was, the solder comes all the way through the joint.

Another  view, same shot.

On this last picture, I took a hammer and drove a scratch awl into the joint. Took a couple of hits.Notice the solder is solid on all the layers.

Here's a picture of the same piece, taken from the back of the piece. This is the bottom. The silver line showing in the joint is where the solder came completely through the joint. Also take note of the discoloration of the metal caused by the heat.

Almost never solder counter-flashing. By definition, it's not in 'direct water flow', like the roof and doesn't require the same techniques.
When making a repair, I use SS wire brush, and 'Stay Clean' liquid flux. Most times though, I end up replacing the bad area. Remaining thickness of metal will be a huge factor too. If copper comes really clean, Amco Oil, Wet-Oil, or Oatey may work fine. Plan on having a variety nearby.
If it's a flatlock type joint, I clean areas, (3" wide), on both sides of the joint thoroughly, then cut the existing joint out. Form new flatlock piece, I side bent 160 degree, other side 90 degrees, hooking hardest side first, then 'tuck' the 90 degree side under. Allow 1/4" play or you'll be working against yourself.

If the metal is green, it might not work at all. Sometimes, what works on a section of copper, might not work 10' away on same piece. Lot of 'ifs' here.
FWIW- I will only work T&M for this type repair.