Sample size recommended for a chi-square test for the variance I have read that chi-square test for the variance requires the sample to be large enough. In this answer: p-value and equivalence testing, the chi-square test for the variance is suggested for a small sample. I have had a look on various websites but I don't seem to find this information. Any insight on what would be (in general) the required sample size to run a chi-square test for the variance?

The test "works as advertized" even for very small sample sizes but is pretty sensitive to the assumption of normality (e.g. it is generally sensitive to changes in kurtosis).
It is notably more level-sensitive than a t-test is to the assumption of normality, and in this case large samples will not tend to mitigate the problem.
As such, many people tend to avoid normal-based tests of variance (chi-squared and particularly F).
Even if you do have near normality, your big worry with small sample sizes (as always) will generally be with power (when the assumptions hold or nearly so, the test works in the sense that it does what it says on the box -- tests the hypothesis at the chosen significance level -- but may nevertheless still have poor power).
If you are confident that you will have a near-normal population distribution (don't use a test of your data to decide this), and you do have a specific effect size you want to detect, and a specific power you want at that effect size and a specific significance level, you can calculate sample size via a calculation involving the noncentral chi-squared distribution. Or simulation can be used (indeed, simulation has some advantages in that you can easily investigate the impact of different circumstances from the assumptions).

If your sample sizes were large (which it doesn't sound like), you might consider bootstrap testing, perhaps.
