How to predict disproportionation products from Frost diagram?
Interesting question. First of all understand what is on the x-axis and on the y-axis. You y-axis is Gibbs free energy/Faraday constant. Choose three consecutive oxidation states, the middle oxidation state, if it lies above the two, is likely to disproportionate.Read more here on Frost and Latimer digram



In your case look at the example of $Mn^{3+}$, if you connect $Mn^{2+}$ and $MnO_2$, $Mn^{3+}$ lies above the two, so 3+ oxidation of Mn is unstable with to disproportionation.

In short, just by using Frost diagram you cannot predict disproportionation of Mn (VII) because if it were to disproportionate, you will need Mn(VIII), which is not shown, so Frost diagram analysis only works for three points and you cannot say anything about the boundary values.