If you follow a few tutorials you should manage to conquer the palette issue.
I doubt either flicster or Civ3Edit "screwed up". It is most likely operator error due to being new to the concept.
There are two basic ways to do a palette.
1) generic (and fast)
2) precise (and slow)
1.1.1) Select a unit with a similar color scheme to yours.
1.1.2) If you need to, you can use Civ3flcEDIT to adjust the frame count to match your unit. (others swear by and get good results with Flicster).
1.1.3) Open the FLC and export the PCX file.
1.1.4) Open the PCX file and paste the BMP you created with SBB into it.
1.1.5) use the same tool you made the PCX with to convert it back to a FLC.
1.2.1) Select a unit with a similar color scheme to yours.
1.2.2) If you need to, you can use Civ3flcEDIT to adjust the frame count to match your unit. (others swear by and get good results with Flicster).
1.2.3) Open the FLC and export the PCX file.
1.2.4) Examine the palette of the old unit and tweak it to better match your unit,
1.2.5) use the same tool you made the PCX with to convert it back to a FLC.
1.3.1) use Flicster or Civ3FLCedit to create a storyboard of the right frame count
1.3.2) Open the PCX file with Photoshop (might work with lesser paint programs)
1.3.3) Examine your unit's death storyboard for color scheme.
1.3.4) Select a couple of color spectrums (ie: grey's, yellows, etc) and set a start color and end color for each spectrum and Photoshop will tween the colors for you (very very fast)
1.3.5) Save this palette to the folder that you opened the PCX from. Be sure to save it under the same name and type as your FLC/PCX tool (Civ3FLCedit or Flicster)
1.3.6) use the same tool you made the PCX with to convert it to a FLC.
2.1.1) Open your units SBB DEATH storyboard.
2.1.2) Save your units SBB DEATH storyboard as palette.bmp or something similar.
2.1.3) Using this copy of the BMP go to adjust your hue & saturation. Do not adjust the master just the CIV color (typically the BLUE) and the Magenta (smoke, etc). Set both of these to grey or black. You don't need to worry about these colors as they will always be in your palette.
2.1.4) Then look for other colors to eliminate and change them to the same shade (grey or black).
2.1.5) Then convert the BMP to an indexed color to see how many colors you still need to remove.
2.1.6) Next carefully select individual colors that are very close and replace the "near" duplicates.
2.1.7) Continue doing this until you are down to 160 colors
2.1.8) Take these 160 colors and add them to the PCX you made. (in Photo Shop this would be in rows 3 through 10, and rows 5-14 in PaintShop)
2.1.9) Save this palette to the folder that you opened the PCX from. Be sure to save it under the same name and type as your FLC/PCX tool (Civ3FLCedit or Flicster)
2.1.01) use the same tool you made the PCX with to convert it to a FLC.