<view class="container">

  <picker mode="date" value="{{date}}" start="{{datestart}}" end="{{dateend}}" bindchange="bindDateChange">

    <view class="picker">

      通行日期：{{dates}}

    </view>

  </picker>

  <button class="mini-btn" type="primary" size="mini" bindtap="chaxuntongxing">查询</button>

</view>

.container {

display: flex;

align-items: center

}

最外层包裹一个container容器，使用flex布局即可

<picker mode="date" value="{{date}}" start="{{datestart}}" end="{{dateend}}" bindchange="bindDateChange">  
    <view class="box">
<view class="picker">  
      通行日期：{{dates}}  
    </view>   
    <button class="mini-btn" type="primary" size="mini" bindtap="chaxuntongxing">查询</button>
</view>
  </picker> 

.box{
  display: flex;
  flex-direction: row;
  align-items: center;
}

加个容器，再写css

用css去控制，代码示例，试试吧

<view class="container">
  <picker mode="date" value="{{date}}" start="{{datestart}}" end="{{dateend}}" bindchange="bindDateChange">
    <view class="picker">
      <text>通行日期</text>
    </view>
  </picker>
  <button type="primary" size="mini">查询</button>
</view>


.container {
  display: flex;
  flex-direction: row;
  align-items: center;
}

view是块级元素，独占一行，所以后面的button会另起一行显示