Yalkut Shimoni (Shemos, sec. 162) gives the birthdates of the shevatim and the ages to which they lived, and Sefer Hayashar (beginning of Shemos) gives similar figures for their ages and adds how many years each lived after the descent to Egypt. Putting these two together yields the order of their birth.
There are variant versions on some of the dates, though, so Feldheim's reconstruction isn't the only one possible. R' Aryeh Kaplan zt"l discusses this whole issue at length in his notes to Me'am Loez (The Torah Anthology) to Parshas Vayeitzei (end of vol. 3b).
I suppose one aspect of it is that it makes sense, for example, that Rachel wouldn't have waited until Yehudah was born before giving Bilhah to Yaakov; as soon as she realized that Leah was pregnant again (with Levi), then that would been enough to establish a chazakah and to take action. Another constraint is that there has to be some time between the births of Yehudah and of Yissachar and Gad, since Leah saw that she had stopped bearing children (Gen. 30:9).
Dinah: Ibn Ezra (to Gen. 30:21) says that she was a twin with Zevulun. There is also an opinion, whose source I can't find now, that Rachel and Leah were pregnant at the same time with, respectively, Yosef and Dinah, and that due to Leah's prayer (Berachos 60a) the fetuses were miraculously switched. (This in fact is one of the sources mentioned by contemporary posekim dealing with issues of surrogate motherhood.) According to this, she would have been the same age as Yosef.
The order in Divrei Hayamim: Malbim there quotes Bereishis Rabbah 73:4, that Dan deserves to be listed before Yosef and Binyamin because he was the direct cause of their birth (i.e., the fact that Rachel gave Bilhah as a wife to Yaakov, so that she would bear some of the tribes, was a critical factor for her own later motherhood).