The kina (elegy, said on the ninth of Av) about Jeremiah's going to ask the avos to pray (kina 21 in at least some versions, 26 in the Artscroll edition) is said before the one about Tziyon's telling him to do so (22 or 27). Why this order?
My Kinos Hameforash notes that indeed this one belongs after the following one. Since Az Bahaloch has the phrase
This 21/26 Piyut starts with אז בהלוך ירמיהו. It's not solid proof since אז can be a poetic way of referring to back then. This is, after all how אז במלאת ספק begins.
Either way. The Medrash of Yirmiyahu Hanavi meeting the "Ishah" does not include telling him to get the Avos. That was put into the Piyut at this point but it is not a quote from Tziyon. The Pirush (again in my קינות המפורש) explains that this part is from Hashem as the Medrash Eicha Rabbah says, which is the only source for this.
These two Kinos are bringing up two entirely different points.The latter, relaying the pain of the Shechina, connects with the one after.