I'm trying to figure out how to flash this part of a shed I'm building that has a peak meeting flush with a larger roof section next to it. But I can't figure out what this sort of roof section is called so I can't seem to find any good information on google. What is this called, or how do I flash it?
You could flash it with 2 pieces of sheet lead, which will stretch enough to feather with sufficient overlap.
You could do the same with sheet copper. It would probably tear a bit, but then solder a small patch over the small tear.
With either copper or lead, you can do it with one piece by folding the sheet onto itself creating a z-fold yielding a triple layer. Start by laying it up the back side of the small gable, then up the rake board, then flat onto the main roof. Then start the z-fold on what will become the lower edge that spans the small gable and onto the main roof. Once formed, you'll want to install it under the rake board. To help see how to do this, form it first with a rectangular piece of cloth, such as a bath towel.
The valley formed by the two lower gables will also need special attention. Cut a narrow triangular piece of sheathing to sit in the valley to create a sloped floor on the valley (that slopes away from the upper gable's wall). From the looks of it, the isosceles triangle would be 4-6 inches across the base, and 18" long (high). The porpuse if the triangle sheathing is to support the flashing. Sheet flashing with z-folds will work there too.
How to flash?? ...with lots of peel-and-stick membrane.
Remember, lap everything in “shingle fashion”, including the peel-and-stick membrane. Be sure to lap the membrane onto the vertical wall section 12” or so and lap the wall moisture barrier over the membrane 12” or so.
Make sure the gable end metal flashing is installed on top of the main moisture barrier under the shingles. (Be sure to turn the membrane down over the rake edge of the roof too.)
Where vertical walls meet flat/sloped surfaces we have always nailed a 1 x 4 along the bottom of the wall. Flat/sloped roof membrane laps up onto the 1 x 4, then nailed a tin "Z" flashing over it. Wall membrane laps down over the flashing.
In your case, just treat the lower sloped area the same? maybe use 1 x 3 or 1 x 2 to make it less conspicuous but you may have to cut down the z-bar.