Hi Islansoul,
In musical theory, all modes Aeolian, Locrian and Phrygian have a 6b and not a 5 #, since they already have a perfect 5th. so, a fortiori, a b13. But, no b13 for the Dorian mode ...
We can hear this beautiful chord Am b13, on the first 8 of the theme: "Ralph's piano Waltz" by John Abercrombie.
And to answer your question, Biab has a problem, or rather a defect, or better a gap, he favors in this case the # 5 to the b6. The new "chord theory" function of "chord builder" is very explicit on this subject. And your question reminds that it is still impossible to write Cb and Fb ... with my Favorite Software, maybe with the 2018 MAC version ... but, one day surely! I spend too good times with Band in a box, for to continue to trust them !!
Finally, I found this list of chords, which dates from 2015,
http://www.pgmusic.com/tutorial_chordlist.htmThank you for your question Islansoul,
Jacques
MacBook Pro (13 pouces, mi-2012) - High Sierra 10.13.4- BIAB 2017-(build 186).