Pack rat species could be removing and caching flowers, but there are many other creatures that might be eating the flowers. 
Let's work on ID'ing what is eating the flowers so we can target a way to prevent that damage.

I really have never seen the animal because it's always at night. It seems to like  bright flowers as it's eaten yellow marigolds, purple daisy, tomatoes plant leaves and petunia plants that were in a pony pack flowers and leaves. I bought a live trap and placed flowers  and one plug of the petunias but it didn't go near the trap  Thought I might try peanut butter.  Thank you

Sheridan Loster

Live-trapping and translocation outside your own yard is not legal, and frankly, it wouldn't be effective -- and that's assuming the animal doing the damage to the plants would fit in your live trap. All the the damage you're describing could be from numerous species, from rodents to rabbits to deer.
I think using some protective exclusion (e.g., hardware cloth dome over a raised bed) would be far more effective and effective regardless of what species is involved. If you or a friend have access to a game/trail camera or even a repurposed ring/wayze/household camera, you'd get more information that could inform future prevention of conflicts around your plants :)