The best option would be to parse the JSON text and create the desired rows before inserting it into the database. You could try to use this query BUT it's VERY fragile :

SELECT 
    d.value as destination_address,
    o.value as origin_address,
    Distance_Text ,
    Distance_Value,
    Duration_Text ,
    Duration_Value
FROM 
    OPENJSON(@json,'$.destination_addresses') d,
    OPENJSON(@json,'$.origin_addresses')  o,
    OPENJSON(@json,'$.rows')  r 
    cross apply openjson(r.value,'$.elements') e
    cross apply openjson(e.value) with ( 
        Distance_Text  nvarchar(20) '$.distance.text',
        Distance_Value integer      '$.distance.value',
        Duration_Text  nvarchar(20) '$.duration.text',
        Duration_Value integer      '$.duration.value'
    ) a
where d.[key]=e.[key]

The JSON text itself has problems. It seems that destination and actual element values must be matched by index, BUT elements are contained in a rows array. What happens if there are multiple rows? Or multiple destinations?

The key column returned by OPENJSON without a schema contains the array index. This can be used to somehow match destination and element data by index, assuming there's only one row.

If there are several rows, e.Key can't be used to JOIN with destination addresses, as it contains the element index inside a single row only.

If each row corresponds to a single origin address we could use a join between o.Key and r.Key to map rows to origins :

where d.[key]=e.[key] and o.[key]=r.[key]

I'm assuming in reality the json you have is an array of elements rather than one. If not so, you can remove one level of OPENJSON. I also assume there's always one origin address.

select  ad.value as destination_address, json_value(x.value,'$.origin_addresses[0]') as origin_address, d.*
from openjson(N'[{
   "destination_addresses" :
   [
      "Straße ohne Straßennamen, 99999 Ort, Deutschland",
      "Straße ohne Straßennamen, 99999 Ort, Deutschland"
   ],
   "origin_addresses" :
   [
      "Straße ohne Straßennamen, 99999 Ort, Deutschland"
   ],
   "rows" :
   [
      {
         "elements" :
         [
            {
               "distance" :
               {
                  "text" : "337 km",
                  "value" : 337183
               },
               "duration" :
               {
                  "text" : "3 Stunden, 36 Minuten",
                  "value" : 12968
               },
               "status" : "OK"
            },
            {
               "distance" :
               {
                  "text" : "397 km",
                  "value" : 397126
               },
               "duration" :
               {
                  "text" : "4 Stunden, 22 Minuten",
                  "value" : 15692
               },
               "status" : "OK"
            }
         ]
      }
   ],
   "status" : "OK"
}]') x
cross apply openjson(x.value, '$.destination_addresses') ad
cross apply OPENJSON(x.value, '$.rows[0].elements') el
cross apply OPENJSON(el.value) with (
    distanceText nvarchar(100) '$.distance.text'
,   distanceValue bigint '$.distance.value'
,   durationText nvarchar(100) '$.duration.text'
,   durationValue bigint '$.duration.value'
,   status varchar(100) '$.status'  
    ) d
where el.[key] = ad.[key]

I split the json by destination addresses, and then split the rows the same way. where el.[key] = ad.[key] makes sure each row from the addresses element matchings corresponding row of "rows".

Output:
| destination_address | origin_address | distanceText | distanceValue | durationText | durationValue | status |
| ------------ | ------------ | ------------ | ------------ | ------------ | ------------ | ------------ |
| Straße ohne Straßennamen, 99999 Ort, Deutschland | Straße ohne Straßennamen, 99999 Ort, Deutschland | 337 km | 337183 | 3 Stunden, 36 Minuten | 12968 | OK |
| Straße ohne Straßennamen, 99999 Ort, Deutschland | Straße ohne Straßennamen, 99999 Ort, Deutschland | 397 km | 397126 | 4 Stunden, 22 Minuten | 15692 | OK |