Depending on the accessibility laws in the UAE, accessibility might be an important point for him as well. While he may not care about accessibility in and by itself, he could face fines for not having an accessible website.
The reasons above should be more than enough to convince them a large percentage of visitors cannot either “see or use” a Flash site, which are typically large in file size and not very visible to search engines.
Basically tell them if its Flash only they’ll lose customers, waste money in unnecessary maintenance costs - find it hard to update - and create accessibility barriers thus excluding and alienating a “large percentage” of users/visitors, etc.