Sorry to hear you have got mold on your roof. We have updated our faq now on our website to include information about tung oil and mold occurring on wood.
Basically, the mold doesn’t affect the structure or the strength or your hive, but it might not look good 
And mold occurs depending on area, humidity etc.
https://www.honeyflow.com/faqs/what-paint-or-varnish-is-safe-to-coat-my-flow-hive-with/p/152#a1
We have heard from one beekeeper experimenting with mold removal, and refinishing. Here are some pictures.
She used Oxygen Bleach (100% Sodium Percarbonate).
Sodium percarbonate is a chemical, an adduct of sodium carbonate and hydrogen peroxide (a perhydrate), with formula 2 Na2CO. 3 · 3 H2O2. It is a colorless, crystalline, hygroscopic and water-soluble solid. It is used in some eco-friendly cleaning products and as a laboratory source of anhydrous hydrogen peroxide.
Once the mold is off you can try using something with a mold prevention in it, or use an outdoor waterproof paint/sealant/stain, etc.
She is in the process of now of testing different finishes on different woods to see how they hold up in the wet weather.
The roof is just natural timber (Inside) with no paint on it and that cleaned up well.
We have one post in our forum explaining all the different types of waterproofing people have tried on their roofs: