I used DocumentDB Data Migration Tool to import one .json file which contains 4 documents and it works well for me.
My .json file :
[
{
"name":"jay1",
"age":20
},
{
"name":"jay2",
"age":20
},
{
"name":"jay3",
"age":20
},
{
"name":"jay4",
"age":20
}
]
And the documents are imported into collection separately.

The JSON file source importer option allows you to import one or more
single document JSON files or JSON files that each contain an array of
JSON documents. When adding folders that contain JSON files to import,
you have the option of recursively searching for files in subfolders.
You could check if you followed the above rules which is stated in the official tutorial to create your .json file. (For example , are your documents in an array?)
Hope it helps you.
Update Answer:
I tired to import data which is followed the format you mentioned in the reply into cosmos db.
My update .json file:
[
{
"id":"001",
"name":"jay1",
"age":20,
"array": {
"a":1,
"b":2,
"c":{
"d":3,
"e": {
"f":4
}
}
}
},
{
"id":"002",
"name":"jay2",
"age":20,
"array": {
"a":1,
"b":2,
"c":{
"d":3,
"e": {
"f":4
}
}
}
},
{
"id":"003",
"name":"jay3",
"age":20,
"array": {
"a":1,
"b":2,
"c":{
"d":3,
"e": {
"f":4
}
}
}
}
]
And the documents are imported into collection successfully.

Update Answer 2:
I followed the format of the document you offered and created 3 sample documents in my .json file.(I just update the '_id' property to 'testX')
My .json file:
[
{
"_id": "test1",
"_rev": "3-99aef1458fe1a8f310c83156b9d06a69",
"delivery": {
"application": "EnvTest",
"sender": {
"id": "[email protected]",
"type": "user"
},
"recipients": [
{
"type": "email",
"recipient": "\"Artzer, Daniel J\" <[email protected]>",
"sentTS": "2018-01-30T19:46:31.515Z",
"id": "45281ab0-05f6-11e8-a86a-61a54dcb42aa"
}
]
},
"payload": {
"startTS": "2017-11-30T07:38:33-06:00",
"equipmentOrLineType": "gathering system",
"scheduledIndicator": "upset",
"field": "Gulf Plains",
"eventDateTime": "2017-11-30T07:31:39-06:00",
"numCopies": "1",
"region": "South",
"facility": "",
"equipment": "",
"causeForRelease": "",
"correctiveAction": "",
"hgbUsed": "no-hgb-available",
"esdActivated": "no",
"submitTS": "2017-11-30T13:38:33.940Z",
"lineSegment": [
{
"lineName": "GPL-1",
"Diameter": "12.725",
"Length": "1000",
"duration": "no",
"volume": "3"
}
],
"creator": "[email protected]",
"savedTS": "2017-11-30T13:38:33.955Z",
"trainingDoc": true,
"_id": "[email protected]_2017-11-30T13:38:33.955Z",
"syncTS": "2017-11-30T13:38:34.794Z"
}
},
{
"_id": "test2",
"_rev": "3-99aef1458fe1a8f310c83156b9d06a69",
"delivery": {
"application": "EnvTest",
"sender": {
"id": "[email protected]",
"type": "user"
},
"recipients": [
{
"type": "email",
"recipient": "\"Artzer, Daniel J\" <[email protected]>",
"sentTS": "2018-01-30T19:46:31.515Z",
"id": "45281ab0-05f6-11e8-a86a-61a54dcb42aa"
}
]
},
"payload": {
"startTS": "2017-11-30T07:38:33-06:00",
"equipmentOrLineType": "gathering system",
"scheduledIndicator": "upset",
"field": "Gulf Plains",
"eventDateTime": "2017-11-30T07:31:39-06:00",
"numCopies": "1",
"region": "South",
"facility": "",
"equipment": "",
"causeForRelease": "",
"correctiveAction": "",
"hgbUsed": "no-hgb-available",
"esdActivated": "no",
"submitTS": "2017-11-30T13:38:33.940Z",
"lineSegment": [
{
"lineName": "GPL-1",
"Diameter": "12.725",
"Length": "1000",
"duration": "no",
"volume": "3"
}
],
"creator": "[email protected]",
"savedTS": "2017-11-30T13:38:33.955Z",
"trainingDoc": true,
"_id": "[email protected]_2017-11-30T13:38:33.955Z",
"syncTS": "2017-11-30T13:38:34.794Z"
}
},
{
"_id": "test3",
"_rev": "3-99aef1458fe1a8f310c83156b9d06a69",
"delivery": {
"application": "EnvTest",
"sender": {
"id": "[email protected]",
"type": "user"
},
"recipients": [
{
"type": "email",
"recipient": "\"Artzer, Daniel J\" <[email protected]>",
"sentTS": "2018-01-30T19:46:31.515Z",
"id": "45281ab0-05f6-11e8-a86a-61a54dcb42aa"
}
]
},
"payload": {
"startTS": "2017-11-30T07:38:33-06:00",
"equipmentOrLineType": "gathering system",
"scheduledIndicator": "upset",
"field": "Gulf Plains",
"eventDateTime": "2017-11-30T07:31:39-06:00",
"numCopies": "1",
"region": "South",
"facility": "",
"equipment": "",
"causeForRelease": "",
"correctiveAction": "",
"hgbUsed": "no-hgb-available",
"esdActivated": "no",
"submitTS": "2017-11-30T13:38:33.940Z",
"lineSegment": [
{
"lineName": "GPL-1",
"Diameter": "12.725",
"Length": "1000",
"duration": "no",
"volume": "3"
}
],
"creator": "[email protected]",
"savedTS": "2017-11-30T13:38:33.955Z",
"trainingDoc": true,
"_id": "[email protected]_2017-11-30T13:38:33.955Z",
"syncTS": "2017-11-30T13:38:34.794Z"
}
}
]
The documents were imported into the db and no error occurred.

If any differences between you and me ,please let me know.