Many child abuse charity websites state this statistic:
A report of child abuse is made every 10 seconds
What is the source of this statistic and is it accurate?
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I think it can be difficult to parse rate information because it's not apparent how those numbers in very relatable terms (everyone can intuit about what "10 seconds" feels like) associate with numbers in very unrelatable terms (I don't believe anyone can quite intuit what a population of 300 million is like, besides symbolically/mathematically).
365 days * 24 hours * 60 minutes * 60 seconds/10 = ~3.2 million reports per year. ~70 million children in the US, so about 1 report per year per 20 children. Since the units are in "reports" and not "children" it could very easily be multiple reports per case. With assumptions for both underreporting and multiple reports of some cases, those numbers seem plausible, and I think that's a more direct way to express the numbers rather than as a rate of individual reports per unit time.
Following the links in your question to the sources they mention (and sources of sources), it seems they're coming from the US HHS (I don't see a year mentioned, but I've grabbed a recent one): Child Maltreatment 2019.
On page 6, they classify reports into those "screened in" and those "screened out":
A referral may be either screened in or screened out. Referrals that meet CPS agency criteria are screened in (and called reports) and receive an investigation or alternative response from the agency. Referrals that do not meet agency criteria are screened out or diverted from CPS to other community agencies.
For the data,
Exhibit 2–A Screened-in Referral Rates, 2015–2019
the latest year, 2019, shows "2,368,325 reports"; they also note that 1.8 children are involved per report.
Exhibit 2–B Screened-out Referral Rates, 2015–2019
the latest year, 2019, estimates "1,625,691 reports", which they also extrapolate to "2,010,000" by a population weighting.
So, depending on which specific number you use and how you think about the different estimates, there are somewhere between 2,368,325 to 4,378,000 reports, possibly involving 4,255,946 to 7,880,400 children.
The claim is not very specific about which reports it's referring to, but 3.2 million is right in the middle of the 2,368,325 to 4,378,000 reports range, and any number of rounding errors or estimations could easily reach the "1 per 10 seconds" reported (which, as calculated above, amounts to 3.2 million per year). I think as long as you recognize the imprecision in the claim, both in numerical precision ("10 seconds", not "10.0 seconds") and meaning of "report", the claim is reasonable.
It's possibly a modest overestimate of the rate if you use the strictest report definition: only "screened-in" reports and not counting number of children involved in a report, 2,368,325/year would be one per 13.3 seconds. Without a more specific reference, like a specific definition, specific year or other recording interval, etc, this seems close enough to me. I've found news sources with references to a number around 3.3 million reports per year referring to the HHS, but it's not clear what specific HHS source those news reports used. For one example of how these strict criteria may not be the best to use, only the most conservative estimate, many of the HHS "screened out" reports are still reports of abuse.