To best respond to the artist's preference for smooth, flowing paint with vibrant color and considering the time she has to finish her commission, the ideal choice of material would likely be oil paint.
Oil paint allows for smooth application, rich, vibrant colors, and offers the flexibility for blending and layering, which can enhance its flowing quality. Additionally, the extended drying time of oil paint gives the artist the opportunity to work on her artwork over many months without feeling rushed.
If you have other options to consider, please share, and I can help evaluate them!