To eyedrop a color and then fill or stroke:
1) Tap Tools icon
2) Select "Paint and Erase"
3) Tap the color button in upper right corner
4) Tap the eyedrop tool
5) Match my color
6) Exit paintbrush tool by tapping done
7) Select my fill layer
9) Turn on fill
10) Tap previous color (which selects the color selected previously with eyedrop tool)
11) Success!
If you added an eyedrop tool on the color select menu for the fill, stroke, etc. tools, you would cut out steps 1-6.