Hi , I really don't know much about this but I do know that when dying cotton with plant dye (flowers , weeds , veggies , etc,) you need to prepare the fabric with a  mordant  before dying.

Perhaps if you researched " Using Plants for dye"the cotton method would work for your canvas.

Mordants prepare the cotton fibres and help them to absorb the dye better.  Mordants  usually give much better, brighter and more permanent colours.  There are different chemicals  you can use as mordants, (most are are very poisonous).  The cotton is first soaked it in a mordant, then dyed ( common mordants are alum, copper sulphate, potassium dichromate, ferrous sulphate and tannin.)  these can be bought in hardware stores or drugstores.
some people mix two together for best results.but I would suggest you research  well before mixing chemicals .

Alum mordant is supposed to give brightest colours and best results and is said to be cheap, Some people use Salt, vinegar and even wood ashes but I have no idea how they do so.
Hope this helps a bit.