Problem:
You are customizing SharePoint Form using the PowerApps.
As you may have noticed, PowerApps Drop-Down menu (Combo box) does not support SharePoint Choice fields property for Allow ‘Fill-in’ choices by the default.

Solution:
In PowerApps, create a logic that stores another text field value to Drop-down menu value. That way you can store the users fill-in choices to the SharePoint List in PowerApps forms.
In my example I have created SharePoint List which contains the following fields:
- Title
- My Drop-down menu (choice field)
- values (choice 1, Choice 2, Other, please give your own value)
- HiddenTextField (Single line of text)
In PowerApps I have set If-statement to the HiddenTextField Visible-property.
If(DataCardValue2.Selected.Value ="Other, please give your own value", true, false)

So, when the user select value “Other, please give your own value” from the “My Drop-down menu”, HiddenTextField is shown in the form.


Then I have set If-statement to My Drop-down-menu (Combo box) Update-event.
If(DataCardValue2.Selected.Value="Other, please give your own value", {
'@odata.type': "#Microsoft.Azure.Connectors.SharePoint.SPListExpandedReference",
Id: 0,
Value: DataCardValue4.Text
},DataCardValue2.Selected)

So, when the item is saved in SharePoint list, PowerApps form takes the value from the HiddenTextField and saves it to the My Drop-down menu as “Fill-in choice”.


Conclusions
That’s it. You can store users Fill-in choices to SharePoint list also in PowerApps forms.