我们可以使用Array.forEach()结合递归函数来做这

let convertData = (data) => {
   let result = []
   data.forEach(d => {
     result.push(d.link)
     if(d.type){
        result.push(...convertData(d.type))
     }
   })
   return result
} 

console.log(convertData(json))

const json = [{
      link: "animal",
      type: [{
            link: "animal/dog"
         },
         {
            link: "animal/cat",
            type: [{
                  link: "animal/cat/savannah"
               },
               {
                  link: "animal/cat/bombay"
               }
            ]
         }
      ]
   },
   {
      link: "car",
      type: [{
            link: "car/dodge"
         },
         {
            link: "car/mazda",
            type: [{
               link: "car/mazda/mx5"
            }]
         }
      ]
   }
]

let convertData = (data) => {
   let result = []
   data.forEach(d => {
     result.push(d.link)
     if(d.type){
        result.push(...convertData(d.type))
     }
   })
   return result
} 

console.log(convertData(json))

您可以使用递归来解决这个问题。

const getLinks = (json, arr = []) => {
    json.forEach(item => {
        arr.push(item.link);
        if(item.type){
            getLinks(item.type, arr);
        }
    });
    return arr;
}

console.log(getLinks(json));

说明：getLinks采用两个参数：json和arr。arr是初始化为空数组的数组。
然后使用forEach循环遍历json数组，并将link属性的值推入arr数组。
如果item具有type属性，则再次调用函数getLinks，将item.type作为第一个参数，将arr数组作为第二个参数。