Is it possible to get animated card from a keg?

Yes, it is possible to get animated cards from Kegs.

However, the rates question appears to be a bit more complicated. My research shows that any information surrounding drop rates from kegs in Gwent are determined using trial and error and a large sample size, since CD: Projekt Red appears to be protective of its drop rate frequencies. However, some dedicated players have attempted to figure out the general drop rates by card type.

While I recognize this doesn't provide an ideal answer to the rates component of your question, I think the only way we will know the animated cards drop rate is with time, and with groups like the ones above taking the time to try and calculate it themselves over time.

As such I will happily revise this answer if/when the rate is finally calculated, however, until then, this spreadsheet tracking the drop rates by card type is to me the best information available on any drop rates in Gwent. This spreadsheet could also be supplemented to find the animated card drop rate if someone figures out the percentage chance of a given card being animated from a keg, though again, until someone trial-and-errors their way into figuring out this number I am not sure we can know the drop rate with any certainty.