When a child is born, it is usually with no medial arch visible. Around the time he starts walking (12 to 15 months of age on average), the longitudinal arch is still not visible. This is not a reason to worry, as most children develop the arch between the age of two and three, and the Pediatric Ortophedic Society of America (POSNA) stated it's not late for the arch to develop even at the age of five . The flat-footedness is entirely normal at a young age.
What causes delays in children's walking?
Parents are often anxious about their children, especially when they notice what’s commonly called variations of normal. What most parents of children with feet abnormalities fail to realize is that the visible foot deformities are rarely to be blamed for delays in walking. The real delays occur when a child has an underlying neuromuscular condition. 
Variety of reasons can attribute to walking delay. Some of them are genetic, such as Down syndrome. Premature birth can also be a cause for developmental delays, as well as conditions such as hip dysplasia. Even seemingly innocent things such as carrying your child a lot instead of letting her practice her walking skills may cause a delay in learning to walk, as well as using a baby walker too much.
What is a flat foot?
Flat feet (pes planus, or fallen arches) is a relatively common condition that has no accurate definition. It is a disorder in which the arch of the feet is much lower than usual. The condition is characterized by collapsed medial arch, abduction of the forefoot, and medial rotation and plantar flexion of the talus. 
In a study conducted among 474 children of primary school age, 22.4 percent of them had flat feet. Boys are twice more likely to have flat feet than girls.  Flat feet usually disappear until the age of six, and only one or two out of ten children proceed into adulthood with this condition. 
The treatment of flat feet
According to a study, flat-footed people have greater muscle tension while walking, while high arches provide greater stability .
If your child’s flat feet trigger pain, he should get plenty of rest an avoid activities that aggravate the condition. There are medications that can help with pain, but avoid giving them to kids, only if absolutely necessary. If a child is overweight or obese, this can worsen flat feet. In this case, losing weigh might reduce some stress on the feet.
Studies have found that overweight or obese children often have significantly lower arch height than children within the healthy weight range. 
There are few types of flat feet and they all can’t be treated the same. If a child has tight Achilles tendon, it can result in flat foot, but this will limit the motion and needs to be treated with heel cord stretches. 
Although rare, there’s a condition that causes problems — rigid flat feet. Moving the foot might be extremely painful, and it can lead to arthritis if not treated on time. This is the kind of flat foot that develops in teen years, never in infantry. Serious as it sounds, this condition indeed requires consulting a pediatric orthopedic surgeon. 
So, do flat feet cause a walking delay?
On the other hand, there are many studies that can confirm link between baby walker overuse and walking delays. A research published in the BMJ stated that baby walker use was strongly linked to developmental delay. For every 24 hours in a walker, a child is another three days later in achieving the ability to walk by herself, an four days later to be able to stand. [11,12]
Feet deformities are not dangerous, and usually don’t affect when a child will start walking, contrary to the belief that most scared parents share. These fears are understandable, and it’s on pediatricians and orthopedic specialists to reassure parents and calm them.