Why did he call Baruch to write the Megilah?
Malbim citing Mahari: All his other Nevu'os, he wrote them himself in a clear expression. Megilas Kinos (Eichah) was not written via Nevu'ah, only with Ru'ach ha'Kodesh 1 , which is a lower level than Nevu'ah. It was necessary to lighten the burden on him, so Baruch wrote it. This is why it says that Baruch read "Divrei Yirmeyah" (verse 10). If it was Nevu'ah, it would be called Divrei Hashem, and not Divrei Yirmeyah! 2
This is why Eichah is in Kesuvim, and not in Nevi'im. (PF)
This Sefer begins "Divrei Yirmeyah"! Perhaps it means matters of Yirmeyah. However, above it says that Uriyah prophesized "k'Chol Divrei Yirmeyah" (26:20)! (PF)