How is 着 pronounced here?
说着 could be either a verb (said) or an adverb (while saying). But as I understand it these are pronounced differently. 


In most cases 说着 reads 'zhe' and means while saying. 

说着(zhao2) is a rare usage only in colloquial language in the Northern dialects, where 着 means hit the target, e.g. '被你说着了' means 'spot on'. The non-dialectal version is '被你说中了'.

Specific to your sentence, 


  曾外祖母做了好饭好菜，说着甜言蜜语，


Without further context, it looks like an incomplete quote because 了 suggests the action of 'making food' was already done at the point soft words were said, the latter must be occurring at the same time with something else that's snipped out. One may naturally think the complete sentence would be like:


  曾外祖母做了好饭好菜，说着甜言蜜语，哄小曾孙子吃。


The soft words were said when great-grandmother was trying to get the child to eat. 着 suggests those actions were occurring in parallel, temporally, and from the semantics we are able to conclude the former is the method for the latter, logically.

Since we know where this sentence is quoted from, we can look at the real context:


  三天里她茶饭不思，精神恍惚，曾外祖母做了好饭好菜，说着甜言蜜语，我奶奶置之不理，宛若木人一样。


There is a time frame (三天), now it becomes clear that 着 suggests it's a repetitive action 'during' those three days as opposed to an one-off action. The whole sentence goes:


  In those three days, grandmother fell into a trance and had no desire to eat. Her mother made good foods and kept saying soft words to her, but she did not respond at all just like a wooden stick.