You should learn flows by heart. Flows work very well, and are best established by starting at one side of the instrument panel or cockpit or airplane, and working toward the other. Or starting at the top and working down, or left to right, and so forth. Know your flows...what you need to check and do, and accomplish these from memory. Then back it up with the checklist.
You should thoroughly know and understand the checklist, and develop your flows from the material in the checklist, but you needn't memorize the checklist itself.
You can develop a flow from each checklist segment. For example, if you have a BEFORE TAKEOFF checklist with 10 items, you can anticipate what needs to be done, do it in a convenient flowing pattern, then review the checklist. You needn't do it in the same order as what's found on the checklist...you just need to cover everything. When it's accomplished, then review the checklist to make sure you got everything.
BEFORE TAKEOFF:
Fuel Selector BOTH
Flight Controls FREE & CORRECT
Throttle 1700 RPM
Magnetos CHECK
Suction Gauge CHECK
Ammeter CHECK
Propeller CYCLE
Transponder ON
Strobes ON
Auxilliary Fuel Pump ON
There is your checklist for an imaginary airplane. 10 items which may or may not be arranged in the way you'd find them in a flow. You might do the flow by bringing your power to 1700 RPM, and starting at the left side of your cockpit with the magneto switches. Next to those are the strobes, and you turn them on. Next to those are your aux pump switches, and those get turned on. Your flight controls are on the way, test them top and bottom. As you move past those you find the propeller control, you cycle it. Your transponder is next to the right, and that gets turned on, and next to that
you find the suction gauge and ammeter...both checked. You've flowed left to right, and all that's left is to go down to the bottom of your pedestle, note the fuel selector position, and you can retard your power to idle, and pull out the checklist.
This is an imaginary airplane, of course; yours will be layed out different. You can see, however, that a simple flow moves in order of convenience in checking the items for that particular checklist segment, and needn't be accomplished in the order that they're found on the checklist itself. If you find you've forgotten an item and discover it when you review the checklist...that's why you have a checklist.