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()

The easiest way to hack through seaborn's, ahem, anti-jet security system is to use mpl_palette directly:

sns.mpl_palette("jet", 6)

The more general approach for "given a matplotlib colormap, how do I get a list of discrete colors?" is to call the colormap object with vector of intensities between 0 and 1:

plt.cm.jet(np.linspace(0, 1, 6))

Note that you'll get different results there because seaborn clips the two extreme values, doing something like

plt.cm.jet(np.linspace(0, 1, 8))[1:-1]

Also, while I agree that jet is a basically fine source for a small number of discrete colors, unless you really need colors specifically from jet for some reason, I'd suggest looking into the "turbo" colormap, which is constructed basically the same way but with better perceptual properties.

"RdBu_r" is a matplotlib colormap. There hence seems little reason to convert it to a list of colors first. Instead just use it as it is.

import matplotlib.pyplot as plt
import seaborn as sns

cmap = plt.get_cmap("RdBu_r")
cmap.set_bad(color='black', alpha=0.5)

sns.heatmap(data, cmap=cmap) 

It seems there is a bug in seaborn that prevents the below idea from working correctly, so falling back to pure matplotlib:

import numpy as np
import matplotlib.pyplot as plt
import matplotlib.colors
import seaborn as sns
# choose 5 colours to create 5 bins
colors = sns.color_palette('rocket', 5)
levels = [0, 200, 300, 400, 600]
cmap, norm = matplotlib.colors.from_levels_and_colors(levels, colors, extend="max")

flights = sns.load_dataset("flights")
flights = flights.pivot("month", "year", "passengers")

fig, ax = plt.subplots()
im = ax.imshow(flights.values, cmap = cmap, norm=norm)
ax.set(xticks=range(flights.shape[1]), yticks=range(flights.shape[0]),
       xticklabels=flights.columns, yticklabels=flights.index)
ax.tick_params(axis="x", rotation=90)
fig.colorbar(im, ax=ax, spacing="propotional")

plt.show()