It's fine to chain a batch job from another batch job's
finish method. In most cases, this will not result in infinite recursion, although this is dependent on the design of your query and any logic behind performing the chained invocation.
When the second batch job executes, it will execute its own query or query locator in the
start() method, and iterate over batches from that query. The results of any database modifications made by the original batch job will be reflected. Since you seem to be working with a deletion job, the records deleted by the first batch job won't present when the second batch job queries against the object.
Note however that a batch job is not subject to the SOQL row limit when using a Query Locator, so it's possible you do not need to chain at all:
If you use a QueryLocator object, the governor limit for the total number of records retrieved by SOQL queries is bypassed. For example, a batch Apex job for the Account object can return a QueryLocator for all account records (up to 50 million records) in an org
Lastly, if you are performing a one-time deletion as a clean up process, you may wish to simply use the Bulk API via the Data Loader rather than writing a batch class. There are some consequences involved if your architecture involves regularly creating and deleting six figures' worth of objects.