Christa, this is just the field I am working in! Which does not mean I have the 100% good advice for Brodie. I don't know much about cats intestinal problems and I also don't know exactly about the origin of Brodie's problem. But if my thoughts can help a bit...

About yoghurt, except if Brodie is allergic to something specific in yoghurt he should not throw up more if you give him some. And it's full of healthy compounds.

Debbie, acidophilus is not the same as the bacteria contained in yoghurt. The acidophilus you take is probably a probiotic and has been selected to have more beneficial effects in the intestine than the classical yoghurt bacteria.

The difference between acidophilus and Pet Flora is that acidophilus is supposed to be adapted to humans and Pet Flora is for cats and dogs, who do not have the same microbes as we have. And I have no idea whether it is good or bad to give human bacteria to a cat! If you decide to try it may be you should give Brodie a dose lower than for humans.
And in any case, yoghurt or other, this is never a short term "treatment". It has to be eaten daily and you will see effects after let's say two weeks or so.

Pet Flora also contains different bacteria, which is expected to be more efficient than only one. But from what I read from the website, they do not explain how they have selected the strains, what the strains are exactly, what the amounts are and if they have tested their safety. You should be careful with these probiotic products because most of them actually do not contain what's claimed on the package. It is already vague for humans but I think it is even worse for animals. Since my previous post I checked a bit more about the available studies in this field...and I could find almost nothing!