'Different result for different browser with CSS

I have different results for different browsers in the following code:

.flexsearch--wrapper {
  height: auto;
  width: 50%;
  max-width: 700px;
  min-width: 100px;
  top: 20px;
  overflow: hidden;
  background: transparent;
  margin: 1px;
  position: absolute;
}

.flexsearch--form {
  overflow: hidden;
  position: relative;
}

.flexsearch--form {
  padding: 0 66px 0 0;
  /* Right padding for submit button width */
  overflow: hidden;
}

.flexsearch--input {
  width: 100%;
}

.flexsearch {
  padding: 0 25px 0 200px;
  /* Padding for other horizontal elements */
}

.flexsearch--input {
  -webkit-box-sizing: content-box;
  -moz-box-sizing: content-box;
  box-sizing: content-box;
  height: 30px;
  padding: 0 46px 0 10px;
  border-color: #888;
  border-radius: 3px;
  /* (height/2) + border-width */
  border-style: solid;
  border-width: 2px;
  /*margin-top: 10px;*/
  color: #333;
  font-family: 'Helvetica', sans-serif;
  font-size: 16px;
  -webkit-appearance: none;
  -moz-appearance: none;
}

.flexsearch--submit {
  position: absolute;
  right: 0;
  top: 0;
  display: block;
  width: 32px;
  height: 32px;
  padding: 0;
  border: none;
  margin-top: 4px;
  /* margin-top + border-width */
  margin-right: 5px;
  /* border-width */
  background: transparent;
  color: #888;
  font-family: 'Helvetica', sans-serif;
  font-size: 30px;
  line-height: 30px;
  -webkit-appearance: none;
  -moz-appearance: none;
}

.flexsearch--input:focus {
  outline: none;
  border-color: #333;
}

.flexsearch--input:focus.flexsearch--submit {
  color: #333;
}

.flexsearch--submit:hover {
  color: #333;
  cursor: pointer;
}

/* UPLOAD ICON IMAGE */

#uploadIcon {
  /*width: 10%;
        height: 100%;*/
  padding-top: 10px;
  min-width: 80px;
  max-width: 80px;
  position: absolute;
  margin: 0 1% 0 77%;
  /*   left : 77%;*/
  top: -3px;
}


/* SIGN UP / SIGN IN*/

.Signin {
  position: fixed;
  /*left: 85%;*/
  margin-left: 86%;
  top: 24px;
  /*border : 1.5px solid grey;*/
  padding: 3px;
  margin-right: 2px;
  float: right;
}

/*#Signup {
        position: absolute;
        left: 93%;
        top: 20px;
        border : 1.5px solid grey;
        padding: 3px;
        margin-right: 3px;
    }
    */

<div class="flexsearch">
  <div class="flexsearch--wrapper">
    <form class="flexsearch--form" action="#" method="post">
      <div class="flexsearch--input-wrapper">
        <input class="flexsearch--input" type="search" placeholder="search">
      </div>
      <input class="flexsearch--submit" type="submit" value="&#10140;" />
    </form>
  </div>
</div>
<a href="#"><img src="upload_icon.png" id = "uploadIcon"></a>
<a href="#" class="Signin">Sign In/Sign Up</a>
<!-- <a href="#" id ="Signup">Sign Up</a> -->

The problem is that arrow and the Sign In and Sign Up with Firefox works perfectly :

Here is the arrow on Firefox. Here is the signIn Sign Up on Firefox.

But with Chrome or Safari it doesn't:

Here is the arrow on Chrome/Safari (they look the same) Here is the SignIn/Sign Up, on Chrome/Safari

Is the problem from my code? or do I need to add some customized code for each browser. And if yes, how can that be done? Can it be done with -webkit or -moz Because I tried this, but it didn't work. Probably, I haven't written it well.

html css

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'Different result for different browser with CSS

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