My Grandma Left Me Her Stamp Collection. Is This Franklin A #596 And Other Ones Valuable?

Welcome.
No, the best assumption is that you have the common varieties, not the other way around. Stamps like you show above were issued in huge numbers, they were the work horses of their time. And with billions of them issued, they are common. If you are interested in the hobby, there are many threads in this community you can read for more info. You can also learn about your stamps here http://stampsmarter.com/1847usa/1847Home.html

here is a link which discussed rare stamp like the 596 (see Appendix A in Article) http://www.stampsmarter.com/learnin...arities.html

Don

The 596 looks pretty close to mine

It also looks like a 552, and a 581. You need to use a perf gauge to measure the perforations and determine if it is flat plate or rotary. It looks like a 552 to me but it would be pretty easy to tell.

Looks like a 632 to me.
The point being "looks pretty close" isn't enough.