What am I missing

Andrea,

Presuming you made the rose parts as (open) stroked paths, depending on how you wish the final artwork to appear, I believe you can:

A) If you wish to have the rose part paths shown in the colours of the background stripes, you can:

1) Group the rose part paths (Ctrl/Cmd+G, hold Ctrl or Cmd and press G);

2) Move the Group from 1) to be on top of the background stripes, select everything, and Make an (Opacity) Mask with both Clip and Invert Mask ticked (Transparency palette);

B) If you wish to have the background stripes shown within the area bound by the rose part paths and have these rose part paths shown in a solid colour (maybe white or black), I believe you can:

1) Group the rose part paths (Ctrl/Cmd+G, hold Ctrl or Cmd and press G), then copy the Group to the front (Ctrl/Cmd+C+F, hold Ctrl or Cmd and press C then F), then hide the copy;

2) Select the original Group and apply two Pathfinders (Pathfinder palette), first Divide, then Unite (Add to shape area) to turn the Group into its outer shape;

3) Show the Group from 1), select both the Group from 1) and the path from 2), and move both to be on top of the background stripes, then lock the Group from 1);

4) Select the path from 2) along with the background stripes, and Make an (Opacity) Mask with both Clip and Invert Mask ticked (Transparency palette);

5) Unlock the Group from 1).

C) If you wish to simply have the background stripes shown within the area bound by the rose part paths without these rose part paths shown in a solid colour, I believe you can:

1) Select the rose part paths and apply two Pathfinders (Pathfinder palette), first Divide, then Unite (Add to shape area) to turn the Group into its outer shape;

2) Move the Group from 1) to be on top of the background stripes, select everything, and make the Clipping set/Mask.

You want the lines of the rose to be visible, but all leaves filled with stripes?

The rose is probably all open paths. You will first need to create closed shapes. At least one closed shape that encompasses all.

Try to make a compound path of the rose outline.