note: Splunk ODBC is a 3rd party software not supported on this forum. You would need to contact the vendor for specifications.
in general OBDC connections do not support concurrent threads. if a connection has a query in progress, be sure the query is completed before another thread starts a new query. connection pooling can help when concurrent threads want to execute parallel queries.
you question implies that each concurrent thread reading data has a dedicated ODBC connection. the maximum number supported will depend on the client resources (max connections, max memory, cpu, etc), server resources, and network bandwidth.