If you defined a SLM policy as the guide said:
PUT /_slm/policy/nightly-snapshots
{
  "schedule": "0 30 1 * * ?", 
  "name": "<nightly-snap-{now/d}>", 
  "repository": "my_repository", 
  "config": { 
    "indices": ["*"] 
  },
  "retention": { 
    "expire_after": "30d", 
    "min_count": 5, 
    "max_count": 50 
  }
}
It should be "easy" to know which snapshot is the most recent one, based on the name.
And if you run:
GET /_slm/policy/nightly-snapshots?human
This will give you what is the latest successful snapshot:
{
  "nightly-snapshots" : {
    "version": 1,
    "modified_date": "2019-04-23T01:30:00.000Z",
    "modified_date_millis": 1556048137314,
    "policy" : {
      "schedule": "0 30 1 * * ?",
      "name": "<nightly-snap-{now/d}>",
      "repository": "my_repository",
      "config": {
        "indices": ["*"],
      },
      "retention": {
        "expire_after": "30d",
        "min_count": 5,
        "max_count": 50
      }
    },
    "last_success": {                                                    
      "snapshot_name": "nightly-snap-2019.04.24-tmtnyjtrsxkhbrrdcgg18a", 
      "time_string": "2019-04-24T16:43:49.316Z",
      "time": 1556124229316
    } ,
    "last_failure": {                                                    
      "snapshot_name": "nightly-snap-2019.04.02-lohisb5ith2n8hxacaq3mw",
      "time_string": "2019-04-02T01:30:00.000Z",
      "time": 1556042030000,
      "details": "{\"type\":\"index_not_found_exception\",\"reason\":\"no such index [important]\",\"resource.type\":\"index_or_alias\",\"resource.id\":\"important\",\"index_uuid\":\"_na_\",\"index\":\"important\",\"stack_trace\":\"[important] IndexNotFoundException[no such index [important]]\\n\\tat org.elasticsearch.cluster.metadata.IndexNameExpressionResolver$WildcardExpressionResolver.indexNotFoundException(IndexNameExpressionResolver.java:762)\\n\\tat org.elasticsearch.cluster.metadata.IndexNameExpressionResolver$WildcardExpressionResolver.innerResolve(IndexNameExpressionResolver.java:714)\\n\\tat org.elasticsearch.cluster.metadata.IndexNameExpressionResolver$WildcardExpressionResolver.resolve(IndexNameExpressionResolver.java:670)\\n\\tat org.elasticsearch.cluster.metadata.IndexNameExpressionResolver.concreteIndices(IndexNameExpressionResolver.java:163)\\n\\tat org.elasticsearch.cluster.metadata.IndexNameExpressionResolver.concreteIndexNames(IndexNameExpressionResolver.java:142)\\n\\tat org.elasticsearch.cluster.metadata.IndexNameExpressionResolver.concreteIndexNames(IndexNameExpressionResolver.java:102)\\n\\tat org.elasticsearch.snapshots.SnapshotsService$1.execute(SnapshotsService.java:280)\\n\\tat org.elasticsearch.cluster.ClusterStateUpdateTask.execute(ClusterStateUpdateTask.java:47)\\n\\tat org.elasticsearch.cluster.service.MasterService.executeTasks(MasterService.java:687)\\n\\tat org.elasticsearch.cluster.service.MasterService.calculateTaskOutputs(MasterService.java:310)\\n\\tat org.elasticsearch.cluster.service.MasterService.runTasks(MasterService.java:210)\\n\\tat org.elasticsearch.cluster.service.MasterService$Batcher.run(MasterService.java:142)\\n\\tat org.elasticsearch.cluster.service.TaskBatcher.runIfNotProcessed(TaskBatcher.java:150)\\n\\tat org.elasticsearch.cluster.service.TaskBatcher$BatchedTask.run(TaskBatcher.java:188)\\n\\tat org.elasticsearch.common.util.concurrent.ThreadContext$ContextPreservingRunnable.run(ThreadContext.java:688)\\n\\tat org.elasticsearch.common.util.concurrent.PrioritizedEsThreadPoolExecutor$TieBreakingPrioritizedRunnable.runAndClean(PrioritizedEsThreadPoolExecutor.java:252)\\n\\tat org.elasticsearch.common.util.concurrent.PrioritizedEsThreadPoolExecutor$TieBreakingPrioritizedRunnable.run(PrioritizedEsThreadPoolExecutor.java:215)\\n\\tat java.base/java.util.concurrent.ThreadPoolExecutor.runWorker(ThreadPoolExecutor.java:1128)\\n\\tat java.base/java.util.concurrent.ThreadPoolExecutor$Worker.run(ThreadPoolExecutor.java:628)\\n\\tat java.base/java.lang.Thread.run(Thread.java:834)\\n\"}"
    } ,
    "next_execution": "2019-04-24T01:30:00.000Z",                        
    "next_execution_millis": 1556048160000
  }
}
You just have to read the value of nightly-snapshots.last_success.snapshot_name.