"e-flier" is a bit of a nonsense term. It means nothing since electronic delivery can be done in so many various ways.
If the client wants a file he can email to perspective people when requested, then a PDF is appropriate. You can embed video, audio, and other interactive elements in a PDF. How you generate the PDF really depends upon what software you have available. Adobe InDesign has many features designed to create interactive PDFs.
If the client wants a "landing page", single web page, or link he can direct people to then standard HTML/CSS markup is appropriate. Basically, it's just a web page. Create it how you would create any other web page.
If the client wants an email to be sent out to perspective people, then using HTML tables is more appropriate. Yes I typed "tables". Email clients are still well behind many browsers. If you want email clients to see things properly using tables is still the best method. You should avoid all background images (some email providers strip them away like GMail) and make all your CSS inline rather than external or referenced in the header. In this case, I can not state emphatically enough that a video in the email is a very poor idea. You should try with all your might to discourage this. It will raise the spam rating of the email considerably. High spam level marks will get the client blacklisted from many email services. Once blacklisted, it can take quite some effort to get white listed again. There are some helpful services for email HTML files such as Premailer which will move styles to inline and other things in preparation for emailing.
Here is a link to check your email for spam ratings.
And here is a link to show what CSS is supported in various email clients.