Dry Cask Storage Act of 2019 This bill requires each licensee of the Nuclear Regulatory Commission (NRC) to submit a plan for (1) transfer (including on-going additional transfers) to spent nuclear fuel dry casks of any spent nuclear fuel stored by the licensee for at least seven years in spent nuclear fuel pools, and (2) configuration of the remaining spent nuclear fuel in the pool in a manner that minimizes the chance of a fire if there is a loss of water in the pool. Among other requirements, the bill requires the NRC to approve or disapprove the plan within 90 days after its submission, authorizes the NRC to provide grants to any licensee with an approved plan to assist in the cost of transferring spent nuclear fuel to dry casks under the plan, directs the emergency planning zone applicable to each civilian nuclear power reactor to be at least 10 miles in radius until all spent nuclear fuel at the reactor has been transferred to dry casks, and requires the NRC to expand to 50 miles in radius the emergency planning zone applicable to each reactor not in compliance with an approved plan.