The inner face of some Roman shields is depicted as being brown or brownish - that could be painted or dyed leather/fabric, or the natural colour of linen or hemp.
I don't think the back of a legionary shield would typically be red or blue if the face of the shield were those colours, as it could easily be seen as a waste of expensive pigment. However Connolly's reconstruction of the scutum from Duro Europos, 1st c. AD, is red on the back (actually scarlet, or orange-red) and many scuta in reentactment groups are painted red front and back.
Einion