I don't remember hearing that the Red Dragon could steal others' power and even use it. How did Issei steal Vali's power? Can the White Dragon steal others' power too?
Issei was able to use Vali's White Dragon Emperor power, Divine Divide, because Issei took one of the jewels in Vali's armor during their fight in Volume 4 and put it on his own. This allowed him to gain access to Vali's predecessors (past Hakuryukou) and their powers.
I picked up the thing lying at my feet—a jewel of the [Vanishing Dragon]. Earlier, when I hit him, his armor was damaged and this thing flew out. His body’s armor seems to have restored the destroyed section including the jewel, though.
I smashed the Sekiryuutei jewel that was on the back of my right hand into pieces, and drove into it the [Vanishing Dragon] jewel that I picked up before! —Your power of vanishing! I’ll transplant it into my Sacred Gear!
He managed to activate it right after he transplanted it into his Sacred Gear.
A hit to Vali’s abdomen with my right fist! In my mind, Buchou’s breasts shook!
At the same time I activated the Hakuryuukou power I had just transplanted and felt the aura covering Vali decrease sharply.
As for the predecessors (refer to my first paragraph), one of the past Hakuryuukou indeed came to him later and helped him during his fight in Volume 10 of the novel.