I know that ArcGIS Online didn't support the GetFeatureInfo of a WMS layer in 2012. But I can't find any updated information about this.
Is it possible to use the GetFeatureInfo in AGOL now? If so... how?
Have a look at this thread.
WMS and ArcGIS Online: Where is the support for GetFutureInfo?
I think the answer is no, WMS GetFeatureInfo is not supported.
Retrieving data ...