The answer is: it depends but generally yes :)
In your example of DynamoDB being used from Azure - yes it is possible.
You will need to create an AWS IAM User with the privileges to use your DynamoDB and use its Access and Secret keys in the Azure-hosted application. That will work seamlessly. Provided your Azure app has internet access, because DynamoDB is accessed over public IP addresses (unless you set up AWS VPC Endpoints, but that's a topic for another discussion).
Likewise Azure Cosmos DB and Google BigTable can be used from all other clouds as well as from e.g. on-prem applications, as long as you provide the right access credentials.
Then there may be services like AWS RDS / Aurora (which is in fact MySQL, PgSQL or similar database engine managed as a service by AWS) which may need some more effort to use from outside. But it's still possible - either you can run it with public IP addresses but then be very careful about setting the right firewall (e.g. AWS Security Group). Or run them on private IP addresses but then you'll need to enable connectivity from your other clouds over some sort of VPN.
Hope that helps :)