Do you have any particular reason for thinking Randyll is a Blackfyre supporter?

It’s mostly a hunch, but these are my reasons:

1. House Tarly is from the Reach, and the Reach was the heart of House Blackfyre’s support. And we know that the Golden Company has friends in the Reach. 
2. Not only is House Tarly from the Reach, but they’re marcher lords to boot, with their castle right across the mountains from House Blackmont. The Marcher Lords were the most anti-Dornish, and thus anti-Daeron and pro-Daemon faction in Westerosi politics.
3. If Savage Sam Tarly and Randyll Tarly are anything to go by, they’d also be attracted to Daemon Blackfyre’s martial persona, and turned off by Daeron II’s bookishness. 
4. Given that I think Aegon VI is going to take the Iron Throne before he comes a cropper, there needs to be something that turns the odds against the Tyrells, and only Tarly defecting would seem to do the job.