Hi @Field ,
Could you please share a bit more about your scenario?
Do you want to filter your SP list records based on the two Choice columns using Checkbox controls?
How do you display the filtered result within your app? Using Gallery control?
I agree with @Anonymous 's thought almost, the ComboBox controls could achieve your needs. If you just want to filter your SP list records using Checkbox controls, I think the combination of Gallery controls and Checkbox controls would achieve your needs simply.
I have made a test on my side, please take a try with the following workaround:


Set the OnStart property of the App control or the OnVisible property of the first screen to following:
ClearCollect(NumberCollection, "Test 1", "Test 2", "Test3");
ClearCollect(WordsCollection, "Test A", "Test B", "Test C")
Add two Gallery controls within my app, set the Items property of the Gallery1 to following:
NumberCollection
Add a Checkbox control (Checkbox1) within your Gallery1, set the Text property of the Checkbox to following:
ThisItem.Value
Set the Items property of the Gallery2 to following:
WordsCollection
Add a Checkbox control (Checkbox2) within your Gallery2, set the Text property of the Checkbox to following:
ThisItem.Value
Then within your app, if you want to filter your SP list reocrds based on the Checkboxes within your Gallery1 and Gallery2, please take a try with the following workaround:
Set the Items proeprty of the Gallery3 or Data Table to following:
Filter(
'YourSPList',
Number.Value in Filter(Gallery1.AllItems, Checkbox1.Value = true).Value,
Words.Value in Filter(Gallery2.AllItems, Checkbox2.Value = true).Value
)
Note: The Number and Words represent the Choice type columns in your SP list.
More details about Filter function in PowerApps, please check the following article:
Filter function
Best regards,