I am trying to understand Speech Act Theory and Biblical Interpretation. What are some good sources on this topic?
Depending on how deeply you want to dive, The Lexham Bible Dictionary is often a good place to start. If you happen to have the Semeia journal, issue #41 is all about putting it into practice.
If you have Wallce's Greek Grammar beyond the Basics: An Exegetical Syntax of the New Testament, he gives a surprisingly good discussion (citing another scholar) about one use of the method in an appendix.
Various handbooks on exegetical methods should also get you started.
What handbooks are you referring to here?