I'm not sure that a booster fan in your HVAC lines will get you the flow you are looking for. I.e. adding a 300 cfm fan in your 6" HVAC line will probably not give 300 cfm total flow, and if I had to guess it would cause problems with cooling in other parts of the basement.
If it were my theater, I would supplement the HVAC line with another supply and return that pull from and exhaust to another part of the basement (i.e. dead vents), each with an inline fan. It's probably overkill, but if you are planning sound isolation, that room is going to be sealed up and you won't have any other air exchange. This does two things, it will supplement your cooling from the AC by pulling cool air from other rooms and exhausting hot air, and it will also keep fresh air moving in.
The issue that Big and Morph1c had is a result of high air velocity. As an example, if you use a 6" flex line connected to a 300 cfm fan then the air in that line is moving at
Cross section area (A) = pi*(r)^2 = pi*(0.25')^2 = 0.196 s.f.
Flow velocity = cfm/A = 300/0.196 = 1,530 fpm
That's way too fast and will be very noisy. If that 6" line connected to your HVAC is only moving 75 cfm, then the velocity drops to
Flow Velocity = 75/.196 = 382 fpm
Still too fast, but then again you can usually hear the air coming out of the registers in your house, so it's a reasonable number I think. Also, if you look at this post, someone actually measured the flow coming from their 5" supply, and it roughly agrees with the numbers we're playing with, and the chart with regard to flow.
So, the solution to all that is to slow down the air before it gets to and/or enters your theater. For the HVAC supply, you're probably OK with a large register as this will allow the air to slow down. For the dead vents, since they will probably be moving more air, you can do what Big and Morph1c did by either adding a few feet of 8" just before your register, or if you have the room, just run a larger duct for the entire length. You can combine this with a lot of area that those ducts have to transition from the duct to the room to help things as well. The higher the cfm, the more cross sectional area is needed. A box is not ideal because turbulent air is noisy, too, but if it's big enough you shouldn't have a problem. Ideally, you would have a smooth transition from your duct to your register (like the shroud on a ducted fan).
Whew! I think I'm getting a repetitive stress injury from all this typing
Of course, all this advice is worth exactly what you've paid for it, so I'd seek a second opinion if you can! My line of work has a lot more to do with electrons than this mechanical stuff 
If it were my theater, I would supplement the HVAC line with another supply and return that pull from and exhaust to another part of the basement (i.e. dead vents), each with an inline fan. It's probably overkill, but if you are planning sound isolation, that room is going to be sealed up and you won't have any other air exchange. This does two things, it will supplement your cooling from the AC by pulling cool air from other rooms and exhausting hot air, and it will also keep fresh air moving in.
The issue that Big and Morph1c had is a result of high air velocity. As an example, if you use a 6" flex line connected to a 300 cfm fan then the air in that line is moving at
Cross section area (A) = pi*(r)^2 = pi*(0.25')^2 = 0.196 s.f.
Flow velocity = cfm/A = 300/0.196 = 1,530 fpm
That's way too fast and will be very noisy. If that 6" line connected to your HVAC is only moving 75 cfm, then the velocity drops to
Flow Velocity = 75/.196 = 382 fpm
Still too fast, but then again you can usually hear the air coming out of the registers in your house, so it's a reasonable number I think. Also, if you look at this post, someone actually measured the flow coming from their 5" supply, and it roughly agrees with the numbers we're playing with, and the chart with regard to flow.
So, the solution to all that is to slow down the air before it gets to and/or enters your theater. For the HVAC supply, you're probably OK with a large register as this will allow the air to slow down. For the dead vents, since they will probably be moving more air, you can do what Big and Morph1c did by either adding a few feet of 8" just before your register, or if you have the room, just run a larger duct for the entire length. You can combine this with a lot of area that those ducts have to transition from the duct to the room to help things as well. The higher the cfm, the more cross sectional area is needed. A box is not ideal because turbulent air is noisy, too, but if it's big enough you shouldn't have a problem. Ideally, you would have a smooth transition from your duct to your register (like the shroud on a ducted fan).
Whew! I think I'm getting a repetitive stress injury from all this typing
Of course, all this advice is worth exactly what you've paid for it, so I'd seek a second opinion if you can! My line of work has a lot more to do with electrons than this mechanical stuff 
















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