Just add some counter in js and use it as a number in id
var count = 3;
$("#add_driver").click(function() {
$("#add_driver_section").append("<div class='wrap-input100 validate-input bg1 rs1-wrap-input100' ><span class='label-input100'>Gender</span><div class='contact100-form-radio m-t-15'> <input class='input-radio100' id='radio" + count + "' type='radio' name='type-product[]' value='male' checked='checked' > <label class='label-radio100' for='radio" + count + "'> Male </label></div><div class='contact100-form-radio'> <input class='input-radio100' id='radio" + ++count + "' type='radio' name='type-product[]' value='female'> <label class='label-radio100' for='radio" + count + "'> Female </label> </div></div>");
count++;
});
<script src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.1/jquery.min.js"></script>
<div class="wrap-input100 validate-input bg1 rs1-wrap-input100">
<span class="label-input100">Gender</span>
<div class="contact100-form-radio m-t-15">
<input class="input-radio100" id="radio1" type="radio" name="type-product[]" value="male" checked="checked">
<label class="label-radio100" for="radio1">
Male
</label>
</div>
<div class="contact100-form-radio">
<input class="input-radio100" id="radio2" type="radio" name="type-product[]" value="female">
<label class="label-radio100" for="radio2">
Female
</label>
</div>
</div>
<button id="add_driver">Add driver</button>
<section id="add_driver_section"></section>
I hope this is what you want to achieve. If not, then let me know.
EDIT
If you want those radio buttons not to act as one radio set, then you need to give them different number.
Here is an example
var count = 3;
$("#add_driver").click(function() {
$("#add_driver_section").append("<div class='wrap-input100 validate-input bg1 rs1-wrap-input100' ><span class='label-input100'>Gender</span><div class='contact100-form-radio m-t-15'> <input class='input-radio100' id='male-radio" + count + "' type='radio' name='type-product-" + count + "[]' value='male' checked='checked' > <label class='label-radio100' for='male-radio" + count + "'> Male </label></div><div class='contact100-form-radio'> <input class='input-radio100' id='female-radio" + count + "' type='radio' name='type-product-" + count + "[]' value='female'> <label class='label-radio100' for='female-radio" + count + "'> Female </label> </div></div>");
count++;
});
<script src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.1/jquery.min.js"></script>
<div class="wrap-input100 validate-input bg1 rs1-wrap-input100">
<span class="label-input100">Gender</span>
<div class="contact100-form-radio m-t-15">
<input class="input-radio100" id="radio1" type="radio" name="type-product[]" value="male" checked="checked">
<label class="label-radio100" for="radio1">
Male
</label>
</div>
<div class="contact100-form-radio">
<input class="input-radio100" id="radio2" type="radio" name="type-product[]" value="female">
<label class="label-radio100" for="radio2">
Female
</label>
</div>
</div>
<button id="add_driver">Add driver</button>
<section id="add_driver_section"></section>
</div>