This company was part of the incestuous pool of Concord, NH, machinery makers. It was in the same building as D. C. Allen & Co., Concord Machine Works, and J. A. White Co.; as ownership varied the name changed every year or two.
The Gear and Dunklee patent listed below is connected to this firm (so far) only through the surname of the latter inventor. There are four patents granted, in whole or in part, to Benjamin F. Dunklee. One of these, an 1873 tablesaw patent, was witnessed by Daniel C. Allen and Frank W. Dunklee. My best guess is the the titular Dunklee & Allen were Benjamin F. and Daniel C., respectively.
The 1874 work, Wiley's American iron trade manual of the leading iron industries of the United States, has a listing for Dunklee & Tilton of Concord, as a maker of machinery.