Starting from this: https://github.com/ngageoint/geopackage-js/tree/master/leaflet
I can see that the GeoPackageFeatureLayer extends L.GeoJSON and accepts all options for L.GeoJSON in addition to three other options: geoPackageUrl,layerName,nocache. This would leed me to searching here:https://leafletjs.com/reference-1.3.4.html#geojson
The GeoJson layer has a Filter property that might be called before adding one particular layer:
A Function that will be used to decide whether to include a feature or
not. The default is to include all features.
Reading from this note: dynamically changing the filter option will have effect only on newly added data. It will not re-evaluate already included features, I take that you will have to have a mechanism for manually updating the added layers to the map.
Coming back to your example, I would try this, updating the feature.properties.property_1 as necessary from the gpk example:
var rivers = L.geoPackageFeatureLayer([], {
geoPackageUrl: 'http://ngageoint.github.io/GeoPackage/examples/rivers.gpkg',
layerName: 'rivers',
filter:function (feature,layer){
if (feature.properties.property_1 == 'Danube') {return 'true'}
},
style: {color: 'green'}
}).addTo(map);
I have also made a JSFiddle with 2 types of filtering the one above, as well as one where property_0 === '6' https://jsfiddle.net/rususorinvick/9ajqhyb3/