Let's break it down:
3 variables at play here will determine this:
1. # of Wickets per Match
2. # of Matches he plays in a year
3. # of years he plays
1.
Assuming this is the peak of Broad's career, let's assume that his wickets/test matches ratio will remain the same (it is around 3.7 right now). Note: This is an aggressive estimate, because this estimate assumes that he will bowl the same # of deliveries per match as he has throughout his career and also will enjoy the same level of performance, not as high of a chance considering he is nearly 30...but let's leave it as this.
Realistic range: 2.5-4 wickets per match
2. # of matches he will play in a year, it is no secret that England plays A LOT of Test matches and Stuart plays in a lot of them. Since he started playing at the end of 2007, he has played 83 test matches, or around 10/year. That is A LOT of test matches without a doubt, and if he remains healthy (which he should as he is not one of those injury prone bowlers CC: Irfan) he should play nearly that amount. So let's assume 10 for this case.
Realistic range: 8-11 matches per year
3.
Stuart Broad is 29, how many more years do you think he has left? Waqar played until age 32, McGrath 37, Wasim 36...this is probably the last time I will try to use Broad in the same paragraph as those 3, but with his fitness, you can expect him to play until he is at least 34-35 aka another 5 years.
Realistic range: 3-7 years.
If we combine all of those together we get a few interesting scenarios:
1. Most aggressive scenario (4 wickets/match, 11 tests/year, 7 years) = 308 additional wickets (exactly double what he has now), making him end up with 616 wickets
2. Range listed in the narrative above (aggressive @ 3.7 wickets/match, 10 tests/year, 5 years) = 185 additional wickets, ending up with 493 wickets
3. Mid-point of realistic range specified above (more realistic @ 3.3 wickets/match, 9.5 tests/year, 5 years) = 156 additional wickets, ending up with 464 wickets
4. Most conservative range (2.5 wickets/match, 8 matches/year, 3 years) = 60 additional wickets, ending up with 368 wickets
Keeping the above in mind, it doesn't seem likely that Broad will be able to break Glenn McGrath's record unless he elevates his game better than how he plays now, plays until he is 36 and England continue to play the same # of test matches as they have done in the past.
Regardless, is it looking like he will end up around the 400 wicket-mark which is a phenomenal feat in this day and age. Against him will be the fact that he is a home pitch bully like his friend Jimmy Anderson and also one of the more hated cricketers of this generation.