A complete Flow URI is unique to the device/install, since is contains the database id of the flow. However, a (Flow beginning) block id/number is permanent.
You can make an complete Flow beginning URI by combining an Flow URI, as returned by the Flow pick block, with the known block id/number:
flowURI++"/statements/"++blockId
to something like:
"content://com.llamalab.automate.provider/flows/1/statements/1"