I am planning on moving to London next spring, 2019 from the USA (I have dual citizenship and a UK passport). I know Brexit officially takes effect in March of 2019. Will this affect my move at all? Will it be easier or harder to find a job (I'm hoping to find a job in London before I move there)? How will the affect the economy, or is it too early to tell?
It certainly is too early to tell how the economy will be effected but with dual-citizenship, you'll be absolutely fine.
UK unemployment is at an all time low, but EU nationals are leaving at an all time high. So it's very difficult to say what will happen after March 2019. All depends on what laws are put in place for EU nationals, visas, etc.
I would suggest making a trip to the UK before you fully relocate. Try and arrange job interviews over the course of a week or a few days and get to know the area a bit during your visit and that will make everything a lot easier and less scary. Bring the family (if you have one).