I think if you were just going out with friends, then mixing colours could be quite fun, but for a wedding...I think you'd look like either a peacock, or like a bag of M and M's had just vomited on you.
What is your colouring like?
I would say that at the very least you would need a pashmina to wear as a shawl to formalise it a bit. You can get them cheaply from all over the place. I think a dark shade of green would suit the dress well, and give you a good base colour to work with.
How formal is the wedding? Because the dress you have is made from a linen/cotton mix, it's automatically going to look more casual. If it's a smarter wedding, you are going to need to play with other fabrics and jewellery to smarten it up a bit. If it's a more casual wedding, then you don't need to worry so much.
Here are three ideas for you:
Green and silver: Dark green pashmina in a silk mix (as above), with strappy silver shoes (I'm not sure any block colour would work well) with silver earrings.
Depending on what look you want to go for, you could go for either these or these, which are both flat, so a little more casual, or these which are more formal.
Green and gold - if you have a warmer colouring, then go for the dark green pashmina (as above) with gold shoes and earrings. Again, Dune have a good collection in gold, as with the silver.
white and Green - Alternatively, go for a white pashmina in a silk mix (the tie shop and accessorize often have pashminas), with a pearl necklace and earrings (fake ones are fine) and white shoes. Again, avoid block colours for the shoes else they risk looking clumpy and hideously old fashioned. Something like these or these should work well.