Triggering the same job twice with the same parameters concurrently using a parallel block causes the two jobs to get the same job number and causes the parallel block to hang.

In the flow script below, ParallelChild1 is just a regular freestyle job with concurrent execution enabled, and one string parameter which is empty by default.

parallel (
  { build("ParallelChild1") },
  { build("ParallelChild1") }
)

The Jenkins console output when running this flow script is:

Started by user PF
parallel {
    Schedule job ParallelChild1
    Schedule job ParallelChild1
    Build ParallelChild1 #70 started
    Build ParallelChild1 #70 started
    ParallelChild1 #70 completed
 

The script then hangs forever. From the Monitoring plugin I can see that there is a thread called "BuildFlow parallel statement thread for Parallel_Debug" which never ends.
The stack trace for that thread is:

BuildFlow parallel statement thread for Parallel_Debug
sun.misc.Unsafe.park(Native Method)
java.util.concurrent.locks.LockSupport.park(LockSupport.java:175)
java.util.concurrent.locks.AbstractQueuedSynchronizer$ConditionObject.await(AbstractQueuedSynchronizer.java:2039)
java_util_concurrent_locks_Condition$await$0.call(Unknown Source)
org.codehaus.groovy.runtime.callsite.CallSiteArray.defaultCall(CallSiteArray.java:48)
org.codehaus.groovy.runtime.callsite.AbstractCallSite.call(AbstractCallSite.java:113)
org.codehaus.groovy.runtime.callsite.AbstractCallSite.call(AbstractCallSite.java:117)
com.cloudbees.plugins.flow.JobInvocation.waitForFinalization(JobInvocation.groovy:259)
com.cloudbees.plugins.flow.FlowRun.waitForFinalization(FlowRun.java:111)
sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)
sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)
sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)
java.lang.reflect.Method.invoke(Method.java:498)
org.codehaus.groovy.runtime.callsite.PojoMetaMethodSite$PojoCachedMethodSiteNoUnwrapNoCoerce.invoke(PojoMetaMethodSite.java:233)
org.codehaus.groovy.runtime.callsite.PojoMetaMethodSite.call(PojoMetaMethodSite.java:56)
org.codehaus.groovy.runtime.callsite.CallSiteArray.defaultCall(CallSiteArray.java:48)
org.codehaus.groovy.runtime.callsite.AbstractCallSite.call(AbstractCallSite.java:113)
org.codehaus.groovy.runtime.callsite.AbstractCallSite.call(AbstractCallSite.java:125)
com.cloudbees.plugins.flow.FlowDelegate.build(FlowDSL.groovy:227)
sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)
sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)
sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)
java.lang.reflect.Method.invoke(Method.java:498)
org.codehaus.groovy.reflection.CachedMethod.invoke(CachedMethod.java:93)
groovy.lang.MetaMethod.doMethodInvoke(MetaMethod.java:325)
groovy.lang.MetaClassImpl.invokeMethod(MetaClassImpl.java:1215)
groovy.lang.MetaClassImpl.invokeMethod(MetaClassImpl.java:1024)
groovy.lang.MetaClassImpl.invokeMethod(MetaClassImpl.java:812)
com.cloudbees.plugins.flow.FlowDelegate.invokeMethod(FlowDSL.groovy)
hudson.util.spring.ClosureScript.invokeMethod(ClosureScript.java:83)
org.codehaus.groovy.runtime.metaclass.ClosureMetaClass.invokeOnDelegationObjects(ClosureMetaClass.java:430)
org.codehaus.groovy.runtime.metaclass.ClosureMetaClass.invokeMethod(ClosureMetaClass.java:369)
groovy.lang.MetaClassImpl.invokeMethod(MetaClassImpl.java:1024)
org.codehaus.groovy.runtime.callsite.PogoMetaClassSite.callCurrent(PogoMetaClassSite.java:69)
org.codehaus.groovy.runtime.callsite.CallSiteArray.defaultCallCurrent(CallSiteArray.java:52)
org.codehaus.groovy.runtime.callsite.AbstractCallSite.callCurrent(AbstractCallSite.java:154)
org.codehaus.groovy.runtime.callsite.AbstractCallSite.callCurrent(AbstractCallSite.java:174)
Script1$_run_closure1.doCall(Script1.groovy:41)
Script1$_run_closure1.doCall(Script1.groovy)
sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)
sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)
sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)
java.lang.reflect.Method.invoke(Method.java:498)
org.codehaus.groovy.reflection.CachedMethod.invoke(CachedMethod.java:93)
groovy.lang.MetaMethod.doMethodInvoke(MetaMethod.java:325)
org.codehaus.groovy.runtime.metaclass.ClosureMetaClass.invokeMethod(ClosureMetaClass.java:294)
groovy.lang.MetaClassImpl.invokeMethod(MetaClassImpl.java:1024)
org.codehaus.groovy.runtime.callsite.PogoMetaClassSite.call(PogoMetaClassSite.java:42)
org.codehaus.groovy.runtime.callsite.CallSiteArray.defaultCall(CallSiteArray.java:48)
org.codehaus.groovy.runtime.callsite.AbstractCallSite.call(AbstractCallSite.java:113)
org.codehaus.groovy.runtime.callsite.AbstractCallSite.call(AbstractCallSite.java:117)
com.cloudbees.plugins.flow.FlowDelegate$_parallel_closure5_closure7.doCall(FlowDSL.groovy:443)
sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)
sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)
sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)
java.lang.reflect.Method.invoke(Method.java:498)
org.codehaus.groovy.reflection.CachedMethod.invoke(CachedMethod.java:93)
groovy.lang.MetaMethod.doMethodInvoke(MetaMethod.java:325)
org.codehaus.groovy.runtime.metaclass.ClosureMetaClass.invokeMethod(ClosureMetaClass.java:294)
groovy.lang.MetaClassImpl.invokeMethod(MetaClassImpl.java:1024)
org.codehaus.groovy.runtime.callsite.PogoMetaClassSite.callCurrent(PogoMetaClassSite.java:69)
org.codehaus.groovy.runtime.callsite.CallSiteArray.defaultCallCurrent(CallSiteArray.java:52)
org.codehaus.groovy.runtime.callsite.AbstractCallSite.callCurrent(AbstractCallSite.java:154)
org.codehaus.groovy.runtime.callsite.AbstractCallSite.callCurrent(AbstractCallSite.java:166)
com.cloudbees.plugins.flow.FlowDelegate$_parallel_closure5_closure7.doCall(FlowDSL.groovy)
sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)
sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)
sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)
java.lang.reflect.Method.invoke(Method.java:498)
org.codehaus.groovy.reflection.CachedMethod.invoke(CachedMethod.java:93)
groovy.lang.MetaMethod.doMethodInvoke(MetaMethod.java:325)
org.codehaus.groovy.runtime.metaclass.ClosureMetaClass.invokeMethod(ClosureMetaClass.java:294)
groovy.lang.MetaClassImpl.invokeMethod(MetaClassImpl.java:1024)
groovy.lang.Closure.call(Closure.java:414)
groovy.lang.Closure.call(Closure.java:408)
java.util.concurrent.FutureTask.run(FutureTask.java:266)
java.util.concurrent.ThreadPoolExecutor.runWorker(ThreadPoolExecutor.java:1142)
java.util.concurrent.ThreadPoolExecutor$Worker.run(ThreadPoolExecutor.java:617)
java.lang.Thread.run(Thread.java:745)