you say you installed the firebird odbc, but the error message clearly says you are using MSDASQL and not LCBI.IBProvider.3, so offhand, i'd say you should script your linked server so we can see the settings you have for it.
for every linked server i've ever set up, i've ALWAYS had to set the two properties AllowInProcess and DynamicParameters for the driver: they are never the right values by default.
for example:
EXEC master.dbo.sp_MSset_oledb_prop N'Microsoft.ACE.OLEDB.12.0', N'AllowInProcess', 1
GO
EXEC master.dbo.sp_MSset_oledb_prop N'Microsoft.ACE.OLEDB.12.0', N'DynamicParameters', 1
this web site has some nice screenshots on usign the GUI to set up a firebird connection/linked server:
http://www.ibprovider.com/eng/documentation/mssql_2012.html
Lowell