Tell your client "no". This is why you are hired.
- Would you ask a chef for his/her recipes so you can "make this on your own"?
- Would you ask an architect to make plans you can "edit on your own"?
- Would you ask a mechanic for his/her tool box so you can "edit your vehicle on your own"?
- Would you ask a doctor for his/her Physicians Desk Reference so you can "diagnose things on your own"?
There's a reason professionals are hired. If the client can "do this on their own" they don't need you - and the request is specifically so they can stop hiring you - nothing more. Which really is not a problem. But that doesn't mean you need to assist in them not hiring you.
If a client wants something they can edit whenever they feel like it, then the client should create the file from scratch. A designer shouldn't be involved if it will be a client-driven design.
The client is merely looking to save money by not requiring your services. Which, again, I understand. However, they don't have the tools nor experience to edit anything you create and ensure all the technical requirements remain met or satisfactory. Or that the integrity of the overall design is kept in tact.
One doesn't ask a professional to "dumb down" something so that services aren't required when changes are later desired. In many instances, because they can't be "dumbed down". Are you going to pack your experience and expertise - all the little things you are aware of but never really think about - into a "Google Doc"?
Example... I hire a lawyer to write my will. The entire reason a lawyer is hired is to ensure the will conforms to all the technical requirements as dictated by law. But I want to also be able to edit the will myself at any time. If I were to edit the will freely afterwards, there's no guarantee or assurance that all the required technical aspects will still be met after my editing. Thus possibly negating the will entirely or creating undesired ambiguity.
So, sure create an editable flier via Google Docs.. then your client can insert 72ppi images they've "borrowed" from the web and enlarge them 150%... Enlarge their logo 200% ... change color(s) ... make the headline bigger ... your name is still on the design...
When someone asked "who created that horrible flier for you".... Do you think the client is going to say they did it themselves? Your reputation is still effected by these new client-driven edits.
Any client who values your work, won't be asking you to "make it so I can edit it" especially for anything print related (web-based content management is more standard and controllable).
If you value your career, you won't create things so that uneducated, inexperienced, unaware, clients can edit your designs - and ultimately have a direct impact on your overall reputation as a designer.
Simply because a client asks for something, that never means you need to bend over backwards to make it happen. Especially if it's detrimental to your business or reputation.
If it were me, I'd apologetically state I can't create anything they can edit, and I'd offer possible solutions so they could create something themselves with minimal expense or learning curve - Word, PowerPoint, or any of a dozen freeware/shareware apps - it merely comes down to what their time is worth regarding learning how to accomplish a design in whatever software they choose.
I also generally explain to such a client that my making a change may be a hour of my time at most (most often much less than an hour).... and that expense is typically far, far, below the cost of any time invested in a learning curve for some other, inferior software. And with my time, the client reaps the benefits of my design sense and abilities. It merely means they can't make changes on a whim free of charge.
I, personally, will also actually suggest they go to some of the online crowdsourcing sites and see if they can find a dirt cheap person to create something they can edit - there is a market for these type of clients and this type of work. However, it's never profitable work for a designer and anyone with any acumen in the field will generally not fulfill such a request. If you take on work like this, you'll never get ahead. I won't put my reputation in the client's hands, but there are countless other naive individuals who haphazardly will.