Flashing should go under shingles and into brick joints so it drains by gravity. Caulking is basically a gap filler.

Well I'm talking about the areas where it connects the brick to the roof shingles. This was supposed to go in under the shingles?

We are considering copper and every time I are this its on top of the shingles. I just want to know if caulking its edges to the shingles and brick is the right way to adhere it.

Is this functional flashing (or decorative)?
Of course it goes under the roofing. You want the water to run off the roofing (over whatever flashing is there) into the gutters. If they just butt up to each other, you are introducing a leak point.

It's functional, not decorative. I just did a google search and found hundreds of images of flashing on top. All the neighborhood houses have it like this too. You can see the step design on the brick, too.

If the roof is sloping where it meets the brick the flashing is installed in pieces called "step flashing". Each piece is bent at a right angle and is inserted between the shingles where they overlap so the flashing is hidden. The top of the flashing pieces are inserted into the joints of the brick and mechanically fastened. This is called "counter-flashing" because there is always a "base flashing" below it which is usually flexible self-adhered rubberized-asphalt flashing (Ice & Water Shield or PERM-A-BARRIER).

Where the flashing meets the brick horizontally the bottom "skirt" of the flashing is exposed on top of the roof shingles.

Caulking should never be used to adhere anything to anything else; it's simply not designed to do that. All weathering joints in a building should be mechanically secured or they will inevitably separate and leak. Caulking is often used to seal a narrow uniform crack or joint and it must be installed with a "backer-rod" so the part that adheres to the materials is thicker than the center of the caulk bead (hour-glass shape in section) but it is never what is keeping the two materials from separating.

I have been detailing flashing on brick buildings for 40 years so I am puzzled that you would be trying to learn about such a difficult subject in an online forum. No offense intended but waterproofing is the realm of experienced builders and designers; not DIYers. When you look at neighborhood houses you need someone with you to tell you what is good and what is bad practice or you are simply wasting your time and effort.

I am trying to make sure out roofer uses best practices when our flashing is installed. My builder told me either we use caulking or solder, but mostly they use caulking. I know nothing of roofing, but wanted to hear thoughts here. I've read articles about this online so I know what kinds of questions to ask my builder before this is installed.

Your comments don't make any sense to me. I'm have a hard time imagining a condition where caulking and solder would be reasonable substitutes for each other. It would help if you told us what condition you are referring to.

Or, posted a picture.

i'm sorry, i don't have a picture, but i'll take some tomorrow.

i obviously don't know the first thing about this, i just wanted to research a little bit so i can help make an educated decision.

There should not be any need to solder the pieces of counter-flashing one to another. They should have the proper overlap not to need sealant of any kind. Like Ren8 says, detailing flashing is a artisan's work and when done right it both looks good and works properly.
Casey