Okay, back to the signature comparison between that on the postcard and that on a confirmed letter from Jesse Woodson James. I don't claim to be a handwriting expert but I think I am better at it than the experts that the Dalton and Bill Anderson naysayers claim to use. I'm attaching the signature from the postcard and one from a letter that Jesse wrote and signed 30 years or so earlier.
On the letter signature, the lower half of the first "J" smoothly flows into the "e" with no space between, exactly the same way the writer of the postcard did. Next, look at the gap between the top and bottom loops of both "J" s in the postcard signature. The same gap is present on the second "J" in the letter. Then look at both signatures and you'll notice that the second capital "J" does not connect with or flow evenly into the "a" in the last name on either signature. If you magnify both signatures, you'll notice that the top of the "a" is open. The "m" s in both signatures are mostly peaked, not rounded. There are other handwriting similarities in the texts of the letter and the postcard also.
~Texas Jay