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I received several responses to my questiin about the gkuten free status of
Annatto:

1.
annatto

annatto also anatto (e-nä´to)  also arnatto (är-nä´to)  noun
plural annattos
1.A tropical American evergreen shrub or small tree (Bixa orellana), having
heart-shaped leaves and showy, rose-pink or sometimes white flowers. Also
called lipstick tree.
2.The seed of this plant, used as a coloring and sometimes as a flavoring,
especially in Latin American cuisine.
3.A yellowish-red dyestuff obtained from the seed aril of this plant, used
especially to dye fabric and to color food products such as margarine and
cheese.

[Of Cariban origin.]

Excerpted from The American Heritage® Dictionary of the English Language,
Third Edition  © 1996 by Houghton Mifflin Company. Electronic version
licensed from INSO Corporation; further reproduction and distribution in
accordance with the Copyright Law of the United States. All rights reserved.

2.
Annatto itself has no gluten, and comes from a plant that is
not related to the grain family at all. However, it is often
mixed with wheat flour, when it is powdered for use as a
coloring agent or a spice, and in this form it can be off-limits.
If used as a liquid, I imagine it might well be in an alcohol
base, although I don't know for sure, but many extracts are.
Alcohol might or might not be gf.

It can be hard to find out what was done to processed
annatto, so lots of us just avoid it, although many folks do
report using the pure annatto seeds in cooking without any
problems. They are gf and should be perfectly safe (unless
you're allergic; some people report that they are, but that is
not a celiac thing, it's separate).

3.
several others said essentially the same thing.

In short, it sounds like it may be a bit questionable at least some of the
time or in some foods if processed.  In my mind, it may be along the lines of
carmel colour and/or vinegars.  This last note is just a personal observation,
not advice.

Chris Woodcock
Wayland, MA