Typically developing children do sometimes show repetitive behaviors that are typical of autism (e.g, hand flapping, body rocking). But, in addition to repetitive behavior, an autism diagnosis is based on delays in language and social development. If there are concerns in these areas, your grandson should probably be evaluated again.
If the only concern is his hand flapping, one could certainly work with him on reducing this behavior. I recommend gently interrupting the flapping as soon as it begins. Also, consider the situations is which he is flapping. If he is flapping when excited, work with him on more socially appropriate ways of showing excitement.
For a child to be on the autistic spectrum they have to have enough characteristics in each area to get a diagnosis. So a child would be observed and assessed by professionals such as a Speech and Language Therapist, Educational/Clinical Psychologist, Occupational Therapist, Clinical Paediatrician etc.
The areas of difficulty (usually called the triad of impairments), is (a) speech (any language delays or disorders), (b) social interaction (problems with interacting with peers, appears to not know how to play or join in), and (c) rigid repeitive behaviours, lack of imagination, need for routines etc (this can show itself in demanding things are always done in the same way, throwing tantrums at changes in routine, not appearing to have flexibility of thought etc).
If your grandson has these types of difficulties then please post again. If he doesn't it is possible to have some traits of autism, but not enough to get a full diagnosis.
The part of your post I recognise as 'possible' (ie. I notice in my own son), is the detail orientated and the need for things to happen as he wants them to.
What is his interaction like with his peers?
Does he have any sensory issues eg. appears over or under sensitive. For example a child might cover their ears at certain noise and then appear deaf when someone calls their name. Does he complain that soft touch hurts him and then appears not to feel pain if he hurts himself. Is he sensitive to smells, tastes, textures of food. Can he wear clothes with tags in?
Is it just the flapping that is concerning you?
Do you feel that his need to adhere to 'his plans' cause difficulties with family arrangements or playing with his peers?
Thank you so much. It is really the flapping that worried me. He does have language skills and does pretty well socially. This has been very helpful.
Thanks so much for your comments. At one time he didn't interact as well as I would like but now seems to do well. During Christmas h really enjoyed playing with his 6 year old cousin for several days. When she left he announced, "I'm very sad because Lindsey had to leave." That made me feel a lot better. He does seem to be a bit sensative but I think the main thing that worries me is the hand flapping and I didn't know if children that didn't have a problem of some sort do this. They are going to be going to Germany for 2 years and I really wanted to be sure he was OK or had what he needs before they go.
Thanks again for your comments.