Not as knowledgeable as JTilley- who is?, but I have used this site for quick reference before. http://tmg110.tripod.com/british1.htm
I really don't know much about this, but my understanding is that whilst colour-coded the ensigns denoting fleets were coming in to use by the 1580s, it was still relatively common for ships to also fly the personal arms of the nobleman on board. Given Golden Hinde's mission and her conspicuous re-naming in honour of her patron, I would suggest that Drake might have flown the flags of his patron, Sir Christopher Hatton, (which included the Hind motif).
Re the positionining of flags the 'Anthony Rolls' are generally regarded as the best contempoary evidence of Tudor flags, albeit they date to the 1540s. (Just found a really good summary of these here http://www.crwflags.com/FOTW/flags/gb-anth.html) http://en.wikipedia.org/wiki/Anthony_Roll These membranes show various styles of flag and pennant and usually in multiple positions- Living in Cambridge I have been lucky enough to see the originals. (along with Matthew Bakers drawings) All I will say is note what to modern eyes is the suprising preponderance of the colour green- this was the livery of the Tudor dynasty.
I imagine (note, I use the word imagine!) Golden Hinde would have carried a fair complement of flags and pennants for when she was 'showing the flag' around the worldl!!
There is at least one date when we can be sure that Elizabeth I's arms flew on board the Hind, viz when she boarded the vessel at Deptfordin 1580 to bestow upon Drake his knighthood for more or less single handedly paying off the national debt in prize money!
Arthur Nelsons ' The Tudor Navy; men and organization' gives a fair indication of the structure and courtly politics played out in the Tudor Navy- which int he context of the history of English nobility I would venture to say was probably the sort of climate in which flags (personal and national) become very important symbols of power.
I'd be interested to know more about the use of the Tudor Rose motif, as it wasn't used much as a flag in the UK, but it was plastered over pretty much everything else in the UK from church ceilings to wooden furniture!
good luck with the restoration. Finally, if you fancy a good brush up on the sort of references available to a modeller interested in ships of that period- this was a very good discussion; http://modelshipworld.com/phpBB2/viewtopic.php?t=2844