How can I avoid conflicts between two immigration petitions?

If the I-829 petition is denied, then you could pursue permanent residency through the approved I-140 petition as long as your employer has not revoked the I-140 petition.

Once you have obtained a conditional green card through EB-5, you may still hold on to your priority. However, it is not unusual that the USCIS may not permit such an action, because you are only entitled to one green card. Advisably, keeping a second option may not be justifiable considering the costs involved in pursuing the two immigrant visas. Consult an immigration attorney on all your alternatives.

Once you get one of those immigrant petitions approved and apply for a green card, the other petition should be cancelled.

As a beneficiary of an I-140 petition and currently in H-1B status, presumably with no visa numbers available under the EB-2 or EB-3 employment-based preference, should you file an EB-5 investor petition on Form I-526 and through adjustment of status obtain your conditional lawful permanent residency, you would have abandoned your H-1 visa status. However, your I-140 petition, unless withdrawn by your employer, would remain an approved petition with an established priority date. If for some reason when you file your petition to remove conditions on Form I-829B, it is denied and you lose your permanent residency, you would still have the option of having a new employer file for H-1B status and be eligible to obtain such status for the remainder of your H-1B period of eligibility. If and when your priority date becomes current, you would still have the option of applying for adjustment of status in the United States based upon an approved I-140 petition with a current priority date, assuming that you have maintained a lawful status.

The I-140 approval does not expire. You keep your priority date, and if the employer confirms the job, you can immigrate with it.

Neither petition will affect the other.

If your I-829 gets denied, you will be placed into removal proceedings where you can renew your I-829 or seek another form of relief, which may include relinquishing your EB-5 CPR and pursuing adjustment based on an I-140. However, once you become a CPR, you can no longer be in H-1B status.

USCIS allows two immigrant visa petitions to be on file at the same time. You can continue to remain in line for the EB-2 visa to become available until your I-829 is approved. If the I-829 is denied, you could file an I-485 (adjustment of status application) based on your EB-2 (Form I-140) approval once a visa becomes available. If the EB-2/EB-3 category is backlogged at the time of the I-829 denial, you could potentially go back on the H-1B visa while you wait for the EB-2/EB-3 visa to become available, assuming you have not maxed out your six-year limit.

You cannot be both an immigrant and an H-1B non-immigrant at the same time.