Season chicken with salt and pepper. Place in a large pot and cover with water. Cook over medium or low heat until done. Remove chicken; cook and debone. Set aside. Mix flour, salt, and water. Roll dough, a little at a time, on well floured board until very thin. Cut into small strips and drop a few, one at a time, into fast boiling chicken broth. Cook two or three minutes and then add more dumplings. Repeat the process until all the dumplings have been used or until there are as many as the broth can absorb. The dumplings should be juicy. Return chicken to pot and cover. Remove from heat and let set a few minutes. Add more seasoning if needed.