When making a boutonniere with more than one flower, you will need to pay attention to which way the flower faces.
Notice that the carnation head in the photo below is facing straight up, and that the alstromeria has been bent slightly to the left so it can tuck under the carnation head.
A side view shows both stems parallel to each other before taping them together.
I started taping the two flowers together right below the alstromeria head. I cut off the wire extending below the carnation in order to keep the boutonniere stem as slender as possible.
I continued taping downward, concealing the newly cut end of the carnation. The two blooms are joined together, fitting snugly with no space between the stems.