Pounds of Food Per Day
According to PrecisionNutrition people tend to eat around 4 pounds per day, though that varies a little bit. So the poundage shouldn't be a significant problem, especially if the critter can distribute that weight around the body.
Fats are associated with better health, are a source of energy, but only 2 need to be included in the diet - Omega-3 and Omega-6.
Fiber is useful for the diet, and is thought to help protect against colon cancers, and does help with the gastrointestinal tract, but isn't necessarily essential, especially if the creatures don't live long enough for cancer to be an issue.
Proteins are necessary for a highly mobile creature, but is present in a number of plants- primarily beans, nuts, and seeds, but also present in some algae and mushrooms
There's a handful of mineral requirements that pretty much demand that the user seeks them out, like salt, potassium, and iron.
Then there's a handful of vitamins that can be provided by plants with Calcium being primarily available through leafy veg or beans and the like.
With the nutritional requirements, we have to rule out any single plant being used as the entire diet. Plus I'm pretty sure that growing anything that has roots longer than a couple of millimeters would be pretty disastrous for a creature without some form of exoskeleton.
Nutrition Side note
All those plants you're growing are going to be taking their nutrients from somewhere, and unless the area directly around them is nutrient rich, they're going to take it from the thing they're growing on.
It takes about 4000 square feet growing food to provide enough for 1 person to eat for a year. Assuming that the average human has about 22 square feet of potential growing area, you'd need about a 18000% increase of surface area to grow enough food to survive for a year.
But that's a bit dependent on the lifestyle of the creature. If you didn't need them to be active in a similar way to humans, they'd end up just being plants, because growing your own food is hard work, and staying still and sucking up nutrients is just significantly more effective for anything that doesn't need to hunt.
To be completely self-sufficient on food that's growing on the critter, no it's quite impossible for something with the size and lifestyle of a human to subsist entirely on food grown on it's body. Plus the evolutionary pressures would push something that lives by growing things on it into a very sedentary life style anyway.
On the bright side though, food grown on the body could be a little bit of additional nutrients (again, presuming short roots that don't penetrate the skin and a nutrient rich atmosphere) and act as just a little boost.
There's downsides to having a lot of surface area for things to grow though, especially for anything with an approximate to blood- fleas, lice, aphids, ants, and all those nasty parasites can make use of the same structures that would be used for the plants by just grabbing on and taking a ride on its new permanent living space. With associated diseases. YAY!