You can't edit the html source code of any wiki page.
But CSS is extremely powerful and efficient — why would you want to do it any other way? Your flannel-ocean theme is CSS itself, after all. And most things are achievable via CSS anyway.
What is it, exactly, that you want to do with your wiki's header? We can help you do that with ease. But first off, I want you to convert your site's CSS to be modifiable and have a history (so you can revert CSS mistakes).
Create the page admin:css
On it, copy and paste the following code:
[[code type="css"]]
@import url(http://static.wikidot.com/v--c644960009f5/common--theme/flannel-ocean/css/style.css?0);
/* Enter custom CSS here */
[[/code]]
Then go to the site manager (admin:manage), select "Appearance", and then select "Themes".
Under the _default category, choose "use an external theme", and type in the text box /local--code/admin:css
Click "save changes", and now your site has the Flanel Ocean theme, except for the admin category for safety reasons.
The reason we do all of that is so that you can easily change your CSS code in one place, the admin:css page, which will also keep a record history of your CSS changes. If you accidentally stuff up your CSS, you can easily click "history" and "revert" — something you can't do in the Site Manager's Theme selection.