Paul, You are confusing layer ids with layer names.This works fine: <map wkid="4326" units="{Units.DECIMAL_DEGREES}" esrilogovisible="true" openhandcursorvisible="true" scalebarvisible="true" zoomslidervisible="false" wraparound180="true" initialextent="14.122885 49.002025 24.145893 54.835812" top="40">
<basemaps>
<layer type="wms" label="WMS example" version="1.3.0" skipgetcapabilities="true" visiblelayers="Gminy,Nazwa_wojewodztwa,Nazwa_powiatu,Nazwa_gminy,Powiaty,Wojewodztwa"
url="http://sdi.geoportal.gov.pl/wms_prg/wmservice.aspx" visible="true"/>
</basemaps>
<operationallayers>
<layer type="kml" label="Wrotków" alpha="0.61" url="https://sites.google.com/site/geoinformacjagajewski/Dzialki%20we%20wladaniu%20G%20i%20L.kml" visible="true"/>
<layer type="kml" label="GlebyWawolnica" url="https://sites.google.com/site/geoinformacjagajewski/GlebyWawolnica.kml" visible="true"/>
</operationallayers>
</map>
Don't forget to click the Mark as answer check and to click the top arrow (promote) as shown below: