Looking at the AT&SF 1910 train, I would say that is probably as fast as you could do it in 1910-1920. The AT&SF has been the fastest Chi to LA route for many years, and I do not doubt that it was in 1910, 20 30, or any other time in the last centtuury. The fast trains that were known in the 1950's (and later) began in the mid to late 1930's. This was when the automobile really began to cut into the railroad passenger traffic. Chicago to New York has always been highly competitive between the New York Central and the Pennsylvania. For many years the best times were in the 33 to 36 hour range. Add 4 to 6 to get you to Boston if going through Albany, and 6 to 10 if going through New York. Only after it became practical to do it in less than two nights or at the least part of the second night did the Chicago to New York drop to around 24 hours.
I would say call it 5 days. Also, remember these are times for the top trains which were mostly extra fare and a lot of the top trains were all Pullman. If you were on any kind of budget, you would not be on these permier trains. Instead you would be on a train that make more stops and took more time. If you are Al Capone or someone equally flamboyant, then maybe you would be on one of the top trains. Otherwise you would be on one fo the slower trains. You would also be on one of these slower trains if you were trying to escape notice by the law. Therefore, calling it 6 days or maybe even 7 may be more reasonable. Without an intermediate stop or two, there would probably be no reason to call it more than 7 days. On teh other hand, that would be 7 days without a bath, and 7 days in th epre-air conditionle era fo being dusted with coal smoke and blown dirt of the field so if finances permitted a stop along the way for a bath and clean air might be a very good thing.
Regardless, to say "two weeks by train" shows a considerable lack of research on the realities of the era. This sort of mistake would suggest that there could easily be many other iisues with the setting in the novel that would reduce its level of realism.