A presence of circular reasoning does not automatically, or necessarily at all, discredit a publication. Circular reasoning may indicate a lack of external support for some argument expressed in a book but not necessarily so. The argument itself can however still be valid, even if the human individual expressing it fails to structure it properly.
As to the case of 2. Timothy 3:16:
When Paul wrote the text in 2. Timothy 3:16, there was of course no "Bible"; there was only what they considered as the holy writings (many of which are in today's Bible).
Firstly it's important to note that Paul did not claim that his own letter to Timothy was part of those writings. What eventually became the "Bible" was decided hundreds of years after Paul's death. From this perspective the penning of his letter to Timothy did not introduce a case of circular reasoning into the holy writings during the first century.
Secondly, and perhaps more importantly, the text in that passage reads more like an encouragement for Timothy to use all parts of those writings for the work that Paul recommended. The passage text itself does not contain any argument(s) supported by circular reasoning.
Now however we may have someone saying that the following is an example of circular argumentation in the Bible:
Question: "How do you know the Bible is true? How do you know it is the word of God?"
Christian Answer: "Because the Bible says it is God's word."
This does not however demonstrate circular argumentation in the Bible.
If anything this is someone's opinion about what a "Christian" bases their faith in, or there could be some Christians who would always only answer the proposed question with a reference to 2. Timothy 3:16.
In either case however this example does not demonstrate the presence of any circular argumentation in the Bible.