Despite Charles II Habsburg (1665-1700) had already started flying as an ensign his Royal Arms superimposed to, or even replacing the traditional Burgundy Cross, it was Philip V Bourbon (1701-1746) who definitely dropped the Burgundy Cross from naval flags.
The new dynasty flags showed since the Sovereign's arms as King of Castile on a plain white field, being white Bourbon dynasty's own livery. Spanish flags now closely resembled to French ones, thus reflecting the Pacte de Famille alliance that would rule the relationship between both countries all long 18th century. The Spanish ensign also served as a pattern to similar designs in other states ruled by Bourbon dynasty --i. e. Naples and Parma.
Sources: «Flags of The World» (FOTW) website, Historical Flags 1701-1785 (Spain)
Sizes: ensign W12 x L18 mm, mast flags W8 x L12 mm, jack W6 x L9 mm, pennant W4 x L48 mm.