Does having a flower bed(s) around the outside walls of the house increase insects inside the home?
The short answer is yes, but it doesn't have to be that way. Flowers provide food and shelter to insects, all kinds, some are actually good bugs that will help eliminate the bad ones. Some flowers and plants support beneficial insects more than others.
The mulch used can be a bigger problem. Bark mulches are usually OK but wood mulches may encourage termites or carpenter ants so avoid those. Its best to leave a 5-6" band around your house with no plants or mulches. This band will discourage insects from crossing and you can further enhance it with various insecticides.
If you want to stay organic, diatomaceous earth would be a good choice for this band. Few insects can cross it without it shredding their bodies. Its like broken glass to them.