/sitecore/api/ssc/item/{itemId}?fields=__Security&database=master&includeStandardTemplateFields=true

"__Security": "au|sitecore\User|pe|+item:read|+item:rename|"

public class AccessController : ServicesApiController
{
    [Route("sitecore/api/ssc/itemaccess/{database}/{itemId}")]
    public IHttpActionResult Get(string database, string itemId)
    {
        // simplified. no null check
        var item = Database.GetDatabase(database).GetItem(itemId);
        var model = new ItemAccessDto
        {
            CanRead = item.Access.CanRead(),
            CanWrite = item.Access.CanWrite(),
            CanCreate = item.Access.CanCreate(),
            CanDelete = item.Access.CanDelete(),
        };

        return Ok(model);
    }

    private class ItemAccessDto
    {
        [JsonProperty("can_read")]
        public bool CanRead { get; set; }

        [JsonProperty("can_write")]
        public bool CanWrite { get; set; }

        [JsonProperty("can_create")]
        public bool CanCreate { get; set; }

        [JsonProperty("can_delete")]
        public bool CanDelete { get; set; }
    }
}

http://mysite/sitecore/api/ssc/itemaccess/master/110D559F-DEA5-42EA-9C1C-8A5DF7E70EF9

Result:
{
    "can_read": true,
    "can_write": false,
    "can_create": false,
    "can_delete": false
}