From personal experience and from experiences of others I've found that you don't need parchment paper or any other kind of special paper within rituals or spell work. If you write your own spell you don't need to use a special kind of paper or anything particularly special within your spell (unless of course you want it then great), anyway H2OFanRikki is right about this and I hope this helps with your magickal endeavours.
I am going to make a Hollywood reference that actually is acurate in some degree to witchcraft with the workings of a spell...and it's "Practical Magic". There are significances behind each item or concept behind a spell, but being creative and adaptive is part of spellwork. When Sandra Bullock and Nicole Kidman's characters were doing their necromantic thing to revive the accidentally killed boyfriend, they needed something white to create the pentacle, so Nicole Kidman goes for whipped cream. Hey, it works!
Let's be honest, what exactly is parchment paper?
Do they mean the paper they used in baking or parchment paper that was used in through history until modern paper making methods were invented?
To my knowledge the only difference in parchment paper and normal printing paper is the methods and machinery used to make it. You can easily find parchment paper in art stores but even then they use modern paper making methods and they come out almost the same as normal printing paper. They usually have a variety of colours, patterns and gsm for you to choose from (gms is the thickness of the paper).
There are also vendors online that sell paper made the traditional way, but its very expensive and I personally don't think it is necessary.
If you want parchment paper for aesthetics, then you can very easily make it yourself from normal printing paper with a few cups of tea or coffee. Get yourself a few sheets of paper, crumple them up in a ball, flatten it out again. Place it in a baking sheet and bake it in the oven at a low temperature with a few cups of coffee and tea for 10 mins. Then carefully remove and dry it with a hair dryer or hang it under the sun.
In my opinion as long as the material of the paper is the same then there is it can be easily substituted. In some spells I cast I require rice paper which I cannot replace with printing paper because there are sacred properties in the rice paper from my teaching, but that is the only time when I would go out to find specific paper.