You pose a series of questions. Let me attempt to answer them all:
The instructions say to provide 40µA per cm2, where does that number
This comes from an article of Itaya and coworkers where they studied the electrochemical synthesis of Prussian Blue. (http://pubs.acs.org/doi/abs/10.1021/ja00382a006) In fact; the website in your question refers to an article in the Journal of Chemical Education (http://pubs.acs.org/doi/abs/10.1021/ed075p881) which in turn refers to the JACS article above.
From my understanding, this number should be seen as an experimental condition. It is given so that the experiment is reproducible.
The TIO material I'm using has a different resistance than the glass
listed, will that change anything?
The material you are using has roughly twice the resistivity as compared to the one used in the experiment. In principle, this would not pose too much of a problem. You can tune your electric system using the variable resistor. Just make sure you stick to 40µA per cm2.
All the pt wire I could find was very pricy so I though I would use a
graphite electrode instead, but all I can find is carbon electrodes.
Is that close enough?
This has already been answered by A.K. The carbon flat electrode should work fine. Though I am not sure whether you can use it repetitively (in multiple experiments).
As a boost of confidence. The procedure you are using is both reported in JACS as well as in J. Chem. Ed.; it should work. If you are conducting this experiment at your university or high school, perhaps someone can give you a copy of the articles to which the website refers. The experimental procedures in these articles can be really helpful in preparing your experiment. Best of luck!