I don't understand what was in Frank's favor, when Younger spent 25 years in prison.
The connection between James and Roosevelt may have been more fleeting then the book you looked at has lead you to believe, and a bit more one-sided.
As usual, context is important when trying to understand a historical reference. The connection here concerning when Roosevelt was running under the Bull Moose party banner in 1912, and after an assassination attempt had taken place. A newspaper article makes the connection to the outlaw:
You can see it is one of over 100 letters sent to Roosevelt offering protection if needed. There is actually record of the polite reply which was sent out by a secretary from Roosevelt's office:
This would make it appear the connection between the two was more of James being a supporter of Roosevelt, but not directly connected by other than an offer of support.
The curious thing is that the letter from Roosevelts office actually predates the assassination attempt, so actually must be in response to some earlier communication...