Agent Orange was a mixture of 2,4,5-T and 2,4-D, but both of which are phenoxy-acetic acetic acid class herbicides.
Second point is dioxin is label applied to a group of chemical chemical structures, with 2,3,7,8-Tetrachlorodibenzo-p-dioxin being the most toxic of the group, but was not the predominant "dioxin" contaminant in the 2,4,5-T used in Vietnam. The elevated "dioxin" content of the Vietnam era 2,4,5-T was due to sloppy process control driven by high product output demand.
A literature search for "dioxin" in 2-4-D resulted in no articles stating at "dioxin" was present in the samples tested. The EPA has made a more definitive statement:
https://www.epa.gov/ingredients-used-pesticide-products/24-d
The detection limit for "dioxin" and specifically 2,3,7,8-Tetrachlorodibenzo-p-dioxin using EC-FTMS is astoundingly small, and in the femtogram per gram range, or 1/1000 of a part per trillion. So when EPA states there are no detectable levels of levels of "dioxin" in 2,4-D the amount that could slip by detection is stunningly minute.
The Wikipedia information
https://en.wikipedia.org/wiki/2,3,7,8-Tetrachlorodibenzodioxin contains a pretty accurate information on the compound.