Flowers only last a week or so anyway so it is probably normal for them to fade to brown at this stage.
Long term health of the tree is different. Some plants will tolerate conditions inside but generally it is too dry and not enough air movement for most species to be really healthy. Cotoneaster are pretty tough but unless conditions can be made suitable they will usually gradually fade away indoors. Outside position will usually make caring for the bonsai much easier long term.