If I understand what you want to achieve, here is what I would do :

Create a new score, with as many staves as the instruments needed :

Bb Trumpet + Bb clarinet 1

Flute + Piccolo

Bb Trumpet + Bb clarinet 2

Alto Sax 1

etc...

In the Scoremanager, define each staff for the appropriate instruments (with transposition, etc...).

Copy staff 1 from the old score and copy it to the Trumpet 1staff (or Bb Trumpet + Bb clarinet 1).

Copy staff 1 from the old score and copy it to the Flute + piccolo staff (check if the range is ok, otherwise transpose 8va up)

Staff 2 -> BbTrumpet + Bb Clar 2

Staff 2 -> Alto sax 1

Etc...

Thank you, Michel. Do you know if there is a way to duplicate a staff? 

AFAIK, there isn't. You just create a new staff (Add Instrument), set up its parameters in the Scoremanager, copy the contents of the first staff and paste them into the second one.

(If there are time or key signature changes in the original piece, you may have to copy the first piece with al its staves -complete measure stacks- in a preliminary step so they are transferred to the new file. Then clean up)

There's going to be a lot of copying and pasting when doing this. I would approach it in two steps. Start with a copy of your original score. Add 5 blank staves for flex parts 1 thru 5. Create your arrangement for the basic flex staves. After the arrangement is complete now add additional blank staves for the transpositions.

For part 1 create a C treble part, a Bb treble, an Eb treble part and maybe an F part.  Do that with the other flex parts creating the appropriate transposition. Once that's complete, check the ranges in your parts and make adjustments.

Thank you Jeffrey. This is essentially what I ended up doing. There was a bunch of things for me to learn as I went, which was great, and also a bunch of program quirks to work around, but I was able to get the basics done fairly quickly.

I quickly learned how to reorder the staves and to use grouping but the grouping feature is erratic. Each time I added a staff, moved it up in the score and joined it to a group, Finale applied random groups everywhere and I would have to go in, try to find them and edit or delete them. It is really strange.

I was amazed to use the Tab feature for Bass. It was great how it automatically worked by pasting the tuba part in. I then had to learn how to get it to play certain positions, but that was not bad.

One trouble I am having is getting the score to fit on the page. No matter how I reduce it in Page Settings, the display is the same, even after I Redraw Screen. Any ideas?

The last and really frustrating quirk is Finale automatically starts itself after I close the program!!! Sometimes it will happen once after closing but at other times it happens several times in a row. Very strange!

I appreciate all of the help from form members. Thank you for sharing your insights.

After entering parameters in the Page Format window, go to Page Layout -> Redefine Pages.

Eric said: One trouble I am having is getting the score to fit on the page. No matter how I reduce it in Page Settings, the display is the same, even after I Redraw Screen. Any ideas?

Instead of Page Settings, resize your page with the % tool. Depending on where you click, you can reduce page, staff, or note sizes.

Thank you Michel. Is there a fit to page option or do I need to just experiment manually with scaling?

Thank you Mike. I will give that a try.

The resize tool worked well and seems handy. Still a bit of trial and error for sizing but not too many steps.