If I emailed someone a question in Spanish about whether I should change something on a form or not, and they responded with "Doy seguimiento..." what does that mean?
Does it mean that "he will get back to me" ?
As for your guess "to get back" it is correct but there is, I think, a closer expression to that in English.
Seguimiento = Follow up.
So he means he will "follow up" this matter.
As I understand it "to follow up" is to try to find out more about it or take action about it and then get back to you.
In Spanish "I'll get back to you" will be more like "Te respondo después" or "Le daré una respuesta más tarde" (I don't have time right now to reply) while "Le daré seguimiento" implies doing some actions before replying.