Final image
To follow along download
dzyneoArt2.ai

1. Download and Open dzyneoArt2.ai in Adobe Illustrator or use your own art

2. Open up the brushes pallete by going to Windows > Brushes. Open the Artistic_ChalkCharcoalPencil Brushes by going to Window > Brush Libraries > Artistic_ChalkCharcoalPencil. Select the Brush called Chalk in the Artistic_ChalkCharcoalPencil pallete and it will show up in the brush pallete.

3. With the pen tool selected draw a diagonal across the art work & apply the chalk brush to the stroke. I chose a stroke size of 2px.

4. With the pen tool selected draw another diagonal across the art work & apply the chalk brush to the stroke. I chose a stroke size of 2px.

5. With the pen tool selected draw another diagonal across the art work & apply the chalk brush to the stroke. I chose a stroke size of 3px.

6. Select all the strokes created & go to the top menu Object > Expand Appearance.

7. Open the Pathfinder
pallete Windows > Pathfinder.
Select everything
CTRL(PC)/CMD(MAC)+A.
In the pathfinder pallete click on merge as shown in the image. Then Select just the stroke color in my case it is pink by going to the menu Select > Same > Fill Color & delete the selection.

8. Now you have your distressed art in Vector Format.