You have to convert a list of colors from seaborn palette to color map of matplolib (thx to @RafaelLopes for proposed changes):
import seaborn as sns
import matplotlib.pylab as plt
import numpy as np
from matplotlib.colors import ListedColormap
# construct cmap
flatui = ["#9b59b6", "#3498db", "#95a5a6", "#e74c3c", "#34495e", "#2ecc71"]
my_cmap = ListedColormap(sns.color_palette(flatui).as_hex())
N = 500
data1 = np.random.randn(N)
data2 = np.random.randn(N)
colors = np.linspace(0,1,N)
plt.scatter(data1, data2, c=colors, cmap=my_cmap)
plt.colorbar()
plt.show()
