Here's a couple of things that have worked for me.
Find something heavy (but not too heavy!) that the wire can easily be tied to. Tie it up and tie the other end around something else, like a nail driven into a joist in the basement or something similar, and let it drop a small distance a few times. (make sure you've tied both ends securely! LOL) Then let it hang freely.
Most wires will straighten out after awhile, some may not. Depends on the type of wire, but that floral stuff is tuff, if it's the same as what my Mom uses.
For a really tuff kink, you can do the roller method someone mentioned above and you can try straightening it out with needle-nosed pliers. Put one end in a vise and tighten it down real good-like.
(wrap something around the wire so it's not flattened) Then bend the kink out with a needle-noser. Using a combination of things may work if only one method does not. Again, depends on what kind of wire it is. Steel wire can be a pup, most others are usually agreeable.
Hope you get "straightened out".
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