Here's what happens

First you use DNA Surgery to turn all Monsters on the Field into Dragons

Next you Summon Lord of D and use the Flute of Summoning Dragon.

Would the DNA Surgery allow me to Special Summon 2 let's say Archiends since it's set on Dragons if it's still up?

No, and the reason is because DNA Surgery only works on face-up cards on the field. It does not alter what the monsters in the hand are.