Unfortunately that was not possible, at least until now where Amazon has announced a new Cameras Recap API that will allow users to call up recorded footage to be watched on the Echo Spot, Echo Show, or other Amazon devices like the Fire TV or Fire Tablets. “Today, we are excited to announce the addition of the Cameras Recap API to the Smart Home Skill API so that your smart home camera skill can enable customers to view recorded smart home camera video feeds on Echo Show, Echo Spot, Fire TV, and Fire Tablets.”
Note that this is an API that developers will need to include in their skills for Alexa, meaning that while the API is available, how quickly developers will take to utilize it remains to be seen. However it seems that cameras made by Ring, ARlo, Cloud Cam, and August already have support so if you are using any of those devices, you should be able to take advantage of this new feature.
Unfortunately at the moment users are only able to pull up the last recorded footage, so if you wanted to pull footage from a specific date or time, you won’t be able to do that yet with Alexa.