After Effects will give you cleaner results….
but if you insist on FCP…
1. Run the Reduce Interlace Flicker action is PS CS2 (go to actions palette and choose Video Actions from the submenu)
2. Make sure your FCP settings are set to BEST motion estimation in the Sequence Settings
3. If needed apply the reduce flicker effect as a last result in FCP
Richard M. Harrington, PMP
Author: Photoshop CS for Nonlinear Editors, Understanding Adobe Photoshop, and ATS:iWork