Beyond the standard issues raised in the general Guide section on Copyright and Intellectual Property Rights (IPR), there are no additional issues to raise for dendrochronological data.
It should be noted, however, that dendrochronological analyses are quite unusual in their reliance on existing reference datasets. Without the open sharing of datasets, each researcher would need to undertake the painstaking task of building highly-replicated chronologies from the present day back to the time period of interest for each new region they work in. For archaeology-based wood research to continue to flourish, dendrochronologists need to continue to contribute datasets to the publicly accessible repositories.
Care should be taken to investigate the copyright and IPR agreements for the repository that you are using. These vary considerably and the details of specific archives is beyond the scope of this guide.