Forces wife here and my 2 kids have had between them 8 schools. They are now ages 8 and 11.
My eldest moved OK at infant school (reception to end of year 2) But once she was 7 that changed. Her reaction to changing schools in year 3 was pretty scary BUT it was more to do with it being yet ANOTHER move than probably just the one move. She started bedwetting, crying constantly and talking of never bothering to make friends again. She was also an absolute expert (but very bored) in pre-historic man and the stoneage as she had done this very thorough project at EVERY school she attended. Sadly this meant she also had gaps in stuff she had missed in other subjects. Just before her 8th birthay we put her in boarding school and WOW it suited her!! Never looked back.
Youngest - moved 4 times in 4 years. Never had any issues. Settled in fine everywhere. Adapted to different routines an totally different schools. Thrived on the new girl status. Luckily didnt over repeat any topics or subjects. She asked to board at the same school as her sister and has just joined - but I reckon if she had been our eldest, boarding would never have become an option or requirement for us because she had no issues.
To move children ONCE - IMO, prolly will have little impact. I appreciate its easy for me to sit here and say that, but I really dont think it needs to be an issue for MOST children. There are some children that dont mix well or are very very shy or lack self confience and then I do think they may have a harder time of resettling. Educationally - I really dont think 1 move will make a hue difference with regards to repeated topics or a missed section fo work. With a bit of effort with the new school you can work out if there are any gaps!
It does depend on the child. Few forces families choose the boarding route and yet they move every 2 years or so. Most kids cope well.
My biggest advice is if you are going to move them - do it 100% positively. Dont dwell on leaving old friends, talk about new friends, the nice park next to the new school, the fact you'll be able to walk/drive to school, they have a nice climbing frame in the playround etc etc. Think about what makes your kids tick - and take it positive to them on that level. You will quake in your boots for them on their first day and maybe shed a tear on their last day (if you dont hate the place) but dont let them see this.
Good luck with whatever you decide!! Sorry for waffling but hope it helps someone!!