I have the same brush and whenever I clean it I either use the daily brush cleaning spray from Sephora or I use a little bit of
warm water and gentle shampoo. I find using as little cleaner as possible works best to avoid the bristles sticking together from
being wet. I also use a wash rag to dry the brush. I use gentle side to side brush strokes on the rag. Hope this helps!
Since this is a small brush, it would probably suffice to spray a cleaner on a lint-free cloth and wipe the brush on it to remove any leftover makeup. For a deeper clean, I usually use a tiny amount of a baby shampoo-water solution on my palm and swirl the brush on it, then rinse, pat dry, and reshape, letting it lay flat to air dry.