It all depends on what you mean by "sign" - as in what forms of signature are legally acceptable in your workflow and jurisdiction.
If the form doesn't have any legal validity, a simple checkbox field will do. If the authenticity of a signature could be challenged, you have to use digital IDs or get them to print and wet-ink sign. Echosign simplifies the digital signature process but it does not have the same level of identity guarantee that a commercially-issued digital ID carries.
The form requires the parents to sign a release form worded as below:
In case of accident or serious illness, I request that the school contact me. If the school is unable to reach me, I hereby authorize the school to transport my child to a hospital for appropriate treatment. I hereby release Beth Emeth and its agents of any liability associated herewith. It is understood that this permission is effective as long as this child is enrolled in school.
What is a commercially-issued digital id and how do I use that?
The problem using digital signatures is each user has to establish a digital ID, and most won't know how or be able to. If you use the EchoSign service, which is not free, the signing process is a lot easier for users. EchoSign is a type of e-signature solution, which is not the same as a digital signture, but they are considered legally binding in the US and Canada, and other locations as well.
Are you really sure about this... Suppose 20% of parents need 30 minutes support/handholding and 5% need 2 hours. Doesn't seem unrealistic. Do you have that much time available? Is this project really going to save time over the traditional pile of paper?
Digital signatures can be immensely powerful and time saving. But it needs training for the end users as part of the project, and a coherent strategy to make a lot of use of these signatures to offset the training costs - definitely not, in my opinion, something to just introduce for a one-off project.